We did veer a little off track.

Something I ran across in the First Edition of the
Pocket Guide to the Empire seems to solidify the case for Svaknir having political motivations for trying to blacken Olaf's name with false accusations. The case is still pretty circumstantial, but it all hangs together nicely.
From the
Pocket Guide: "Founded during Skyrim's long Alessian flirtation, the Bards' College continues to flaunt a heretical streak ...". Wulfharth was a hero in part because he cleansed Skyrim of the Alessian heresy in the middle of the First Era, so the
Pocket Guide seems to be saying that the original bards were Alessians. I see no other reason for mentioning bards, heresy, and Alessians in the same sentence. But why would Alessians select Solitude as the site of their college? My guess is that Solitude as a whole accepted and supported the Alessian Doctrines, as did others in Skyrim at the time, so the religious/political climate was favorable to the founding bards.
Now we come to the crisis: High King Borgas, an Alessian himself, is killed by the Wild Hunt for that reason, and the Wars of Succession begin when the Moot fails to name Jarl Hanse of Winterhold as the next High King, though he seems to have been the best candidate. Why not? One good explanation would be that there was a division of religious sentiment among the jarls, so they could not come to an agreement on Hanse, as some desired an Alessian successor and others the opposite. Eventually Olaf One-Eye wins the war and becomes High King.
This might well explain why Solitude attacked Winterhold, assuming that Hanse was not Alessian. By removing Jarl Hanse, they had a chance to get their own jarl on the throne and continue the prevailing Alessian policy that they favored.
Even Viarmo admits that the real history says that Solitude attacked Winterhold without provocation, but the only choices we are given to fill in "Olaf's Verse" all blame Olaf for the attack while painting Solitude as the innocent victim of his wickedness. It looks very much like "Olaf's Verse" comes down to pure propaganda created because of Svaknir's pique at being on the losing side of the squabble. The bards, not to mention the rest of Solitude, were put out by having their Alessian ambitions thwarted, and the whole effigy-burning tradition got started because of that.
Unfortunately, while it appears that we have good reason to doubt the truth of anything Svaknir put into "Olaf's Verse," it doesn't help us establish the real truth about the capture of Numinex.