Paarthurnax should be the most reliable witness, but he tells you nothing about the capture, only that the poor creature was driven mad by his captivity and had forgotten his own name. However, Paarth also tells you that he used to visit the captive. Really? Did he get a visitor's pass from the Jarl, or did he disguise himself as one of the cleaning women? This claim sounds a bit suspect.
When arranging the capture of Odahviing, Balgruuf may mention that the dragon skull above his throne is actually that of Numinex. (I think you have to take the Imperial side in the rebellion to have this bit of dialog show up.) If so, then Numinex must somehow have died or been killed. Yet Viarmo may tell you that Numinex is known to have escaped, depending on your verse suggestions during "Tending the Flames". So we don't know the real truth here, either. Perhaps Numinex simply died in captivity, or he was killed during an escape attempt, or tracked down and killed after escaping. Perhaps the skull is really that of some random dragon and the idea that it is from Numinex came about because it makes a better story.
King Olaf's Verse doesn't seem very trustworthy, either. Svaknir may have had other issues with Olaf -- say a family member killed during the fight over the succession -- and used his position as a bard to spread nasty accusations about his enemy's rise to power. (Note to politicians: it can be a bad idea to make enemies in the media.

The Bard's College perpetuates the accusations to this day and has treated Olaf as The Bad Guy for hundreds of years. However, one of the bards mentions that history is not made by those who act, but by those who write about those acts. A rather cynical and Orwellian comment, but certainly true. If the bards of the time wanted to show solidarity with one of their own, they might have let the story stand and started the tradition of burning Olaf in effigy, so it proves nothing about the truth of the matter. Modern bards are just accepting the accuracy of what has been handed down to them through the college. The only independent study that we have -- Olaf and the Dragon -- doesn't even attempt to do more than lay out the various conflicting stories.
When you meet Olaf in Sovngarde, he refers to Svaknir as an "honorable enemy" and doesn't bear any grudge. It's hard to believe that Olaf would even BE in Sovngarde if he were the cowardly con-artist that the verse makes him out to be. Tsun must have judged him valorous enough to enter the Hall. That seems to speak in his favor. But, then again, Svaknir is there too.
In short, we can't trust the scholarship and we can't ask the living/dead/undead witnesses (Paarthurnax, Olaf One-Eye, and Svaknir) for the full story when we meet them. We can't even get confirmation as to whether Olaf is a Tongue, which would argue for or against the shout-battle legend. No fair, Bethesda! Leaving a mystery in the backstory is one thing, but teasing us with witnesses that we can't question is going too far.
