Except of course that Baltar was actually innocent of the charges they brought.
He had not willingly collaborated with the Cylons, he had tried and failed to get them to back-off, and the major testimony against him was from Gaeta who lied, neglecting to mention the fact that when Baltar signed the order to terminate the dissidents he literally had a gun to his head, and that he'd also volunteered to try to stop Deanna from detonating the nuke, probably saving hundreds of lives.
He had done a lot of things but only the audience was aware of it, not the characters, apart from Roslin's certainty that she had seen Baltar with Six on Caprica.
This is all true. Baltar, as far as anyone knew, was a major asset who had saved their hides on many an occasion, but he only scraped through by a narrow margin - and that was probably because Lee sent the judges on a guilt trip. Sounds like the former colonials had a death urge of sorts (which would explain a lot of other things).