Sheogorath may not necessarily be the Champion of Cyrodiil but he at least had to be someone who knew about the ongoing events in Cyrodiil
"you know, I was there for that whole sordid affair. Marvelous time! Butterflies, blood, a fox (The Grey Fox), a severed head (The head of Mathieu Bellamont's mother)..."
Maybe Sheogorath was the character who became the grey fox and the listener of the dark brotherhood. How else could he have known of the severed head?
In my opinion it's pretty clear that Sheo is the character who entered the Shivering Isles, not necessarily the CoC but still a character from Oblivion.