I decided to test my memory. Here is that Moyers-Beisner exchange from the program's transcript:
"BILL MOYERS: Are you aware that the Acton Institute for years has received steady support from Exxon-Mobil?
DR. CALVIN BEISNER: I became aware of that about oh, three or four weeks ago, I think .... But, frankly, it doesn't have anything to do with the truth of the premises, or the validity of the inferences in the arguments. And that's where we have to focus - is on the arguments."
I was pretty close! Would that Beisner had followed his own sound advice.

Fair point, NW. I guess my only quibble is that Moyers has characterized Beisner's statement as a "lie." Not mistaken or erroneous, but a lie. Accordingly, it does seem both fair and important to respond "I believed it when I said it," if that is true. Now perhaps you are right that more is on order. But if Beisner continues to think that his quote was accurate, albeit subject to some uncertainties or doubts, what should he do? As I understand it, Beisner has stated that he is willing to now rely on Moyers' statement that he is not a Democrat. Perhaps, if true, he should also admit that his recollection is less than precise and it is possible that he was in error, and that therefore he is inclined to rely on Moyers' recollection which seems to be more confident. My impression is that Beisner is pretty close to having said just that, but Moyers hasn't made it easy by uncharitably and unnecessarily assuming a poisonous state of mind.

NW, Are you saying that Beisner could not have made an honest mistake?
No worries, Mike, but I was careful to say just the opposite:
"An honest mistake (giving the benefit of the doubt here) is still a mistake ..."
"Fair enough. He did so 'honestly from the best of [his] memory.'"
I do believe in giving the benefit of the doubt to both men, absent some reason not to.
I had a chance to listen to a podcast of Moyers's piece last night, by the way. I found it very worthwhile, if for no other reason than he was airing a Christian Evangelical point of view that we don't hear about very often. And he did, after all, air Beisner's more publicized point of view as well.
Personally, I like to hear well-made arguments even when I don't ultimately agree with them.
I did find one passage somewhat ironic in light of the present controversy. Moyers asked if it wasn't true that Beisner's group was financed by Exxon, and Beisner fairly responded (paraphrasing here from the best of my memory) that that was irrelevant, as people should examine the substance of one's arguments rather than their source.

NW,
Are you saying that Beisner could not have made an honest mistake? In other words when on our honeymoon my wife asserted that I had told her when we were dating that I was a Republican, she must have been a liar because (i) I knew with 100% certainly I was not a Republican and (ii) I knew with 100% certainty that I would never have falsely stated that I was a Republican? It is not possible that she inferred from my expressed conservative policy preferences that I was a Republican and just mistakenly processed my statements in a way where she mistakenly recalled me saying something I did not say?
Don't you find it at all interesting that the motive you ascribe to Beisner would not place any advantage in using the word "Democrat" instead of "liberal"?
My take on this is that Beisner probably made an honest mistake and Moyers was understandably miffed because he does value the pretense of journalistic integrity. While his real complaint is grounded in the broader accusation of bias, the foot fault was Beisner's mistaken use of the word "Democrat." In fairness to Moyers, while this may have been a foot fault to Beisner since it was not remotely essential to his point, it is important to Moyers, who even if he cannot reasonably expect to avoid the liberal tag, does value his non-partisan (in the proper narrow sense) reputation.
But heck, I'm just guessing. If Moyers said what Beisner said he did, then Moyers would have a strong motive to be an unequivocal liar. But I'd rather assume both men are being basically honest.

do you posit that Moyers has eidetic memory?
Moyers, again, is unequivocal. He's not hedging with, "honestly from the best of my memory ...."
His certainty does not require a photographic memory, because Moyers knows to a 100% certainty whether or not he is a "Democrat," and he knows to a 100% certainty whether or not he "intended for the documentary to influence the November elections to bring control of Congress back to the Democrats," and therefore he knows to a 100% certainty whether or not he went around telling people that he is or that he did.
If, as he says, Moyers truly is not a Democrat, then does anyone honestly think that -- having absolutely nothing to gain by the lie -- he would tell someone that he is? To what end?
Now Beisner, on the other hand, went out of his way to publish what he did about Moyers for a reason -- specifically, to support his admonition of, "Don't expect good science, economics, or ethics--or even journalistic balance." Fair enough. He did so "honestly from the best of [his] memory."
But when his memory was challenged, he had to admit that: "While I understood from the conversation that he was a Democrat, I accept his representation that he is an independent."
So it's not "he said / she said." It's Moyers said / Beisner made some assumptions of fact that he's not prepared to stand behind. (As opposed to his opinions, which he's entitled to.)
He made a mistake and therefore should gracefully apologize and make amends. "I believed it when I said it" isn't quite that.
Criticizing someone is one thing. Misquoting him for the purpose of criticizing him for what he (never) "said," is terribly unfair.

"This is transparently a state-of-mind defense." If you know of anybody who could honestly say more than "I didn't lie but wrote honestly from the best of my memory" without the help of some recording device or contemporaneous notes, will you let us know who that might be? Could Moyers? Or do you posit that Moyers has eidetic memory?

I didn't lie but wrote honestly from the best of my memory.
This is transparently a state-of-mind defense. Hiding behind a technicality, when the real issue is whether the substance of Beisner's allegation was fair to Moyers, who unequivocally says he did not say the things attributed to him.
An honest mistake (giving the benefit of the doubt here) is still a mistake, and one should apologize and try to make amends.
People are entitled to their own opinions about Moyers or anyone else. They are not entitled to their own facts.

Looks like a case of one man's word against another's and I guess I'll let it go at that.

Dr. Beisner should indeed be more careful in attributing comments to Bill Moyers if he can't really recall what he said. I hate it when journalists do that, and blogging is a form of journalism.
That being said, and after reading Mr. Moyer's response below, I think Dr. Beisner is not far off the mark. It seems that his mistake was inserting the word "Democrat" rather than just using the word "liberal".
I suspect the heart of what Mr. Moyers is really upset about is Dr. Beisner's assertion, "Don't expect good science, economics, or ethics – or even journalistic balance." This is Dr. Beisner's opinion, which he has every right to express. And after reading the response of seasoned journalist Bill Moyers, where he writhes in pain like a professional soccer player feigning injury while pointing his finger to "The Right", I agree.