It is impossible to enter SI without being forced into the MQ of Oblivion. You are that same prisoner that witnessed the death of the Emperor, there is no way around this.
The only things Sheogorath says are these lines:
* You know, I was there for that whole sordid affair. Marvelous times! Butterflies, blood, a Fox and severed head... Oh, and the cheese! To die for. -Sheogorath Skyrim
* But only half right. I'm a mad god. The Mad God, actually. It's a family tittle. Gets passed down from me to myself every few thousand years. -Sheogorath Skyrim
I am sorry but that is no hard evidence that This Sheogorath is in fact the "Champion of Cyrodiil" or the "Hero of Kavatch", remember that he is a daedra God so he knows a lot of whats going on in the mortal plane, his first quote means that he is aware of the things that happened in the Oblivion Crisis, while his second Quote means that who ever entered through the portal in the Shivering Isle defeated Jyggalag and became the Mad God... we just dont know if it was the Hero of Kavatch.
Another example could be the Dark Brotherhood, you really think the Hero of Kavatch could have done all of those monstruocities? lets bring the Gray Fox into account, you think he would be willing to join the Dark Brotherhood when we all know Thieves Guild prohibit murder?
The quests were out there in Oblivion for the player to choose what to do, not necessarily means that THE CHAMPION did each and every single Quests out there, but this also does not means that the GrayFox quest and the Dark Brotherhood never happened, in the contrary Bethesda made it quite clear all these things did happened in the Oblivion Crisis, what i think it happened is that while the Champion was doing quests related to the Oblivion Crisis some Thief was doing the quests for the GrayFox and later became the GrayFox (who ever this thief was) and while this happened someone was asked by Lucien to join the Dark Brotherhood and all that stuff happened.
Just a week ago i found a Book in Skyrim which pretty much tell the story of Knights of the Nine, how they rebuild themselves and fought Umaril to his defeat and they never ever mentions the Champion of Cyrodiil... i just cant seem to find the damn book again, gona keep trying but if this the case then its a good sign that the Champion had his hands full with the Oblivion Crisis, and i also doubt he would even became the GrayFox and the head of the DarkBrotherhood and even had defeated Umaril too, thats just too much stuff for a single person, think about it you honestly think the Champion would do all that much evil stuff the Dark Brotherhood does or do all that much stuff Sheogorath requested from him? because Sheogorath is not a "Good" daedra and he is been known to be quite evil at times-