Who else but the CoC was there for every single one of the events Sheogorath lists? I'd also like screenshots wherein this character is present.
http://cloud-2.steampowered.com/ugc/468612597616391389/94D447B503DC5ADF04013CAC79A37062792B7A24/
You are more than free to imagine it being someone else, but to outright deny it was the CoC is another beast entirely.
We know that lore-wise only the main quest should be seen as actions of the titular hero.
Everything else are events that may or may not have happened, but you cant say they are events that are accomplished by the hero.
For instance in Morrowind, ultimately it does not matter what the hero does with the fighters guild - thieves guild tensions, as canon history dictates that the Camonna Tong wiped the thieves guild off the map.
There is absolutely no reason to assume all events in a game happened by agency of the titular hero.
There is a trend going on where people increasingly are insisting on declaring one thing or the other canon or non canon, but TES lore simply does not work that way.
When thinking about events in TES history a certain degree of ambiguity is paramount.
Even in-game sources regularly directly contradict each other.
You can talk in terms of likelyhood and probability, almost never certainty.