I assume what people say is factual to the best of their knowledge, but no one states all the facts and two different people can start with the same facts and arrive at opposing positions. What this means is that proving that a person's facts are technically correct, is not adequate to accept that person's argument.
Even when one agrees with the basic conclusion of the argument one might be annoyed with the way it was presented.
Here is the scene from
Bowling for Columbine where Moore interviewed Charlton Heston displaying a card proving he was a lifetime NRA member and even praising Canada that it had more guns than the US but fewer murders using guns. All of this lead up to Moore asking that Heston apologize for appearing at an NRA rally in Flint after a child was killed by another child with a gun. I may be wrong, but I suspect Moore was misrepresenting himself, that is stating "facts" about himself, to Heston that were not true.
http://www.youtube.com/watch?v=Q1iuEcu7O50
It seems that Moore's argument is that it is OK for Heston to exercise his US right to bear arms, which he explicitly acknowledged, but it was not OK for Heston to exercise his right to freedom of speech. Now, that is something that I would disagree with. I assume that Moore's facts about the murder rate in Canada and the US are correct, but those facts are irrelevant to what he was apparently showing.
I recall thinking that Heston behaved himself better than Moore in that scene.
Moore doesn't need propaganda from his enemies to discredit him. He does a good job discrediting himself on his own.