You can watch the segment online at The Rachel Maddow Show, but for those who can't watch the video, I have transcribed the entire segment and include my own commentary.
The segment opened with a series of clips where Rachel is asking previous guests on her show, “Did I get anything wrong?” This is something I’ve always admired about Rachel Maddow. She’s not afraid to make mistakes, and actively asks if she has made an error because what is important to her is getting the facts right. After playing those clips Rachel explains:
The reason I ask that question of guests on this show sometimes is because inevitably when you are spending 6,000 words a night explaining the news, inevitably some of your words will be wrong. So like last night, there was this amazing moment at the end of our lead story where I say goodnight to our guest and he says goodnight, and I think it’s over and then he says really loud and obviously not to me, he says “There is an error.” This is a very strange moment. Watch.
[Replays video from previous night where guest says, “There is an error. Hello?”]
Hello? I couldn’t see him. I didn’t know what was going … it wasn’t … and he was right. There was an error. That was a really strange way for me to find out about it but it’s true.
[On Screen: Image from News Article: Florida Law on Drug Tests for Welfare Is Struck Down, by Frances Robles, The New York Times, December 31, 2013 ]
The story that we were doing there was about a Federal Court order about Florida’s Drug Test the Poor Law, and I had characterized it as an action by a Federal Appeals Court when in fact it was an action by a Federal District Court. So really there was an error. He was right. And I’m very sorry that there was an error. You never like to get stuff wrong, but it does happen from time to time. And when we get stuff wrong on this show, I try to make sure that we correct it. I don’t mind making corrections. That said; don’t push it.
It's this determination to get the facts correct, even the minutest detail, that makes watching The Rachel Maddow Show so appealing. Also the fact that she goes into so much detail, filling in back stories you never hear anywhere else.


Rachel Maddow: "We cover a lot of right wing politics on this show."
We cover a lot of right wing politics on this show. I mean nothing against Democrats; nothing against liberals, but the selection of stories that we cover on this show reflects my belief as the host that the most interesting story in American politics this decade is the effort by the Republican Party to remake itself in the wake of the disastrous Bush-Cheney Era. And the divides in the party, and the divides particularly within the Party itself, and the Conservative movement that thinks it controls the Party; I think those are the most interesting and consequential fights in American politics today. And I think that the resolution of those fights, who’s going to win and who’s going to lose, is truly an open question and a fascinating and important one for who we are as a country.
This explains another reason why Rachel's reporting is so compelling. She is intellectually curious herself about what's going on with conservatives today, and this causes he to dig deep for answers to what is going on and who is behind it. And the best part is she actually shares what she discovers with us.


Rachel Maddow: "And the Conservative political figures who you can most count on to threaten
to sue you and call your boss and scream about their victimization as loud as they can whenever they
get mentioned by name in a way they do not control are of course, the Koch brothers."
So we cover the Conservative movement a lot on this show, and in so doing we occasionally find people who have been mentioned in our coverage who are absolutely outraged that they have been mentioned in our coverage; people who are not used to being talked about by someone who does not take their instructions. And so what happens is they tend to try to instruct me as to how I ought to talk about them. And the Conservative political figures who you can most count on to threaten to sue you and call your boss and scream about their victimization as loud as they can whenever they get mentioned by name in a way they do not control are of course, the Koch brothers. Charles and David Koch, who inherited a privately held oil and chemical company from their dad, and thereby, became almost unimaginably wealthy. If Charles and David Koch were one Koch brother instead of two; if they were one guy, they would in fact be the second richest guy on earth.
I added the emphasis there because hearing that part made me wonder. I'm a loyal watcher of The Rachel Maddow Show, so I've seen more than a few segments where she has done in depth reporting about the Koch brothers and how they have financed numerous conservative causes, think tanks, activism, etc. Now maybe I've missed a show in the past, but this is the first time I've seen her actually respond on screen to receiving a notice from the Koch brothers. She says "you can most count on to threaten ..." Doesn't that say it has happened before? If it has happened before, and she had responded, wouldn't the Koch brothers know that their idle threats would only cause Rachel to talk about them more, thereby bringing more unwanted attention? How many times have we seen that movie where demanding a retraction of the truth only shined more light on what the person making the demand didn't want talked about?


Rachel Maddow: "When David Koch ran for Vice President on the Libertarian Party line in 1980,
he minted gold dimes with his own head on them, as a campaign trinket."
And they have been political figures as long as they have been richer than God. When David Koch ran for Vice President on the Libertarian Party line in 1980, he minted gold dimes with his own head on them, as a campaign trinket. The Koch brothers have so much money, one of the Koch brothers literally made his own money with his own head on it as a means of trying to persuade you to vote him into the White House. Wow! That’s the level of money, and that’s the level of politics at which these guys have always operated. And when you operate at that level, I think maybe you are not used to hearing things that you do not want to hear; particularly things about yourself. And so, very frequently, when we cover the Koch brothers, we then hear from the Koch brothers’ lawyer.
Wow! Just wow! It boggles the mind to wonder what it must be like to live a life where you always get your way and nobody ever dares cross you. I just keep picturing temper tantrums that children throw when they don't get their way. What is the equivalent for men in their seventies?


Lebron v. Wilkins (PDF)
Our lead story last night was about that Florida Drug Test the Poor Law, which was smacked down by a Federal Judge on New Year’s Eve. The law’s been blocked by the courts twice now.

State Pays Back Thousands After Drug Testing Struck Down, by Kathleen Haughney,
Sun Sentinel, Tallahassee Bureau, August 31, 2012
It was hugely expensive when it was in effect, and it turned out that when it was in effect ...

Welfare Drug-Testing Yields 2% Positive Results, by Catherine Whittenburg, The Tampa Tribune, August 24, 2011
... it turned up levels of drug use by the poor in Florida that were roughly one-quarter the level of drug use in the population at large.So the Florida Drug Test the Poor Law has been an expensive and embarrassing failure from the very beginning. It has failed as a fiscal policy. It has failed legally. It has failed as a bolster for the stereotypes on which it was based. Nevertheless, the political right in this country has successfully marketed that failed Florida policy to lots of other states.

Drug Tests of Welfare Recipients Prove Costly, by Chris Serres,
Minnesota Star Tribune, December 27, 2013
AND
Kansas Follows Missouri’s Path in Testing Suspected Drug Users on Welfare,
by Brad Cooper, The Kansas City Star, December 26
We highlighted local reporting last night from states like Missouri and Kansas and Minnesota, who have all adopted versions of the failed Florida law and are all now either reaping the negative consequences of their laws or are worried that they’re about to.This is an interesting political question, right, about how obviously failed policies nevertheless get picked up and moved into different states even as they fail everywhere they are tried. And it is therefore an interesting political question as to, who does that? Who tells states that they ought to do what Florida did with a policy like this?
Are you paying attention Koch brothers? This is what started the ball rolling on this story. Rachel wondered why anyone would promote and continue to promote a policy that is an abysmal failure in one state in other states, expecting a different result. Have you ever heard Einstein's definition of insanity?

RELEASE: Think Tank Shares Florida’s Welfare Drug Testing Success at Georgia Public Hearing, Florida Foundation for Government Accountability, February 15, 2012
Well, in the case of this Florida law that we looked at last night, it’s a group called the Florida Foundation for Government Accountability. They went to public hearings in Georgia, to share the good news about Florida’s terrible policy and why Georgia should adopt it.

RELEASE – Think Tank Featured at ALEC Health and Human Services Task Force, Florida Foundation for Government Accountability, December 5, 2011
They went to a national meeting of the group ALEC in Arizona to market Florida’s terrible policy to state legislators from all over the country. Quote ALEC members should look to Florida for free market Medicaid and welfare reforms.
Wait a minute. Did I just hear that correctly? "[L]ook to Florida for free market Medicaid and welfare reforms." Isn't "free market" another way of saying "private sector?" So maybe the goal behind these laws has nothing to do with the public good or saving the states money, and everything to do with lining the pockets of private companies. Somebody was paid to administer those drug tests.

Florida SPN Members
So who is this group telling state legislators from all over the country that they ought to adopt Florida’s terrible law? Turns out they’re part of a huge network of state based conservative think tanks that is frankly kind of designed to not look like a network.

State Policy Network Directory
They all look vaguely indigenous. They all have what look to be locally specific names. But their funding, if you follow it, comes in part from a central source of big money corporate donors, including groups affiliated with the Koch brothers.


Report: Think Tanks Tied to Kochs, by Tal Kopan, Politico.com, November 13, 2013
AND
Koch Brothers Plan More Political Involvement for Their Conservative Network, by Nicholas Confessore, The New York Times, April 30, 2013
AND
Koch-Funded Group to Hit Trio of Vulnerable Dems Over Obamacare Support, by Clara Ritger, National Journal, January 2, 2014
AND
Americans for Prosperity puts big money on legislative races in Arkansas, by T.W. Farnam, The Washington Post, October 1, 2012
AND

Exposed: The Dark-Money ATM of the Conservative Movement, by Andy Kroll, Mother Jones, February 5, 2013
AND

Koch-backed group launches new attack on health care law, by Fredreka Schouten, USA Today, September 19, 2013
AND

Tax Filings Hint at Extent of Koch Brothers’ Reach, by Nicholas Confessore, The New York Times, September 12, 2013
Now we are not the first news outlet to report on the Koch brothers funding distribution networks, and the groups small and large all over the country who’ve received funding through the various mechanisms that the Koch brothers have set up to support conservative candidates, and conservative activism, and conservative research, and conservative advocacy. And the Koch brothers’ lawyers are not denying that they fund these networks or that the Florida Foundation for Government Accountability is one of the groups that has been funded through these networks. But they really do not want anyone reporting any connection between what those groups do and who gives them the money that they do it with.

Rachel Maddow: "I’m not going to read their script. I’m not going to renounce my own reporting
on this story because the reporting on this story stands. It is true."
The Koch brothers’ letter to us includes a script that they want me to read to you on the air denouncing my own reporting on the Florida Drug Test the Poor story and telling you [reading from script] "that they are not involved in promoting any such issue."I’m not going to read their script. I’m not going to renounce my own reporting on this story because the reporting on this story stands. It is true and now we also know that the Koch brothers do not wish to be associated with the work and the causes that they have funded through their multi-million dollar, multi-year massive funding of networks of conservative organizations. You not wanting to be known for something that you have done is not the same thing as you not having done it. The Koch brothers do also say that when we contacted them for comment on our story, it was too late in the day for them and that we should have given them more time to respond. And you know what, that is a fair point. We will endeavor in the future to contact them earlier in the day and I’m sorry that our call came late.
And now the part you've been waiting for, where Rachel tells the Koch brothers how life works for the majority of Americans. I encourage you to read slowly and savor every word.
But we will not stop reporting on the political actions and the consequences of the political actions of rich and powerful men even if they send angry letters every time we do it. I will not read scripts provided to me by anyone else. I do not play requests. I will happily make corrections when I do get things wrong. We do it on this show all the time. But I will not renounce or retract reporting that is true even if the subjects of that reporting don’t like it.Being a political actor means being subject to political scrutiny. If you don’t want to be known for it, DON'T DO IT. Don’t just complain when people accurately describe your actions. Your actions are what we are reporting on and we will do that on our own terms as a free press. If you want to control the words that are used when your actions are discussed, then speak for yourself. I will renew my invitation now. Mr. Koch, or the other Mr. Koch, you are welcome on this show any time. I would love to discuss these matters with you right here, in person, live and without interruption, any time. It would be easy to set up. You apparently already have my number.
And so the Koch brothers set out on a mission to persuade Rachel Maddow to retract the truth she told, and in doing so even more people than those who happened to catch the opening segment of Thursday night's show know more about the Koch brothers than they did before.With that, Rachel closed the show with the obligatory introduction of this weekend's showing of episodes of Lockup, which means that The Rachel Maddow Show only aired once tonight. This was a huge motivating factor in my determination to transcribe every word so that even more people will either read the transcript or watch the segment.


That does it for us tonight. We appreciate you being with us. Happy New Year! We’ll see you again on Monday. I do have to tell you though that before you can go to your weekend you do have to spend some very important quality, quiet time in prison.