I'd guess that canonically, the Champion of Cyrodiil also completed the main storylines of Shivering Isles and Knights of the Nine, in the same way, I believe that the Nerevarine also completed the main storylines of Morrowind and its two expansions (in fact, the story of Tribunal kind of has to be completed by the same person as the one who fulfilled the Nerevarine prophecies for it to make sense.) as far as the non-mainquest related faction questlines, I don't think it's ever said if these quests were completed by the same person as the main quest or not, so I'd say that it's fairly ambiguous and is up to players to decide. While those events probably actually happened, they don't necessarily have to have been fulfilled by the same person as the one who was central to the main storyline. So yes, I'd say the "Those things happened in canon but might not have been done by the same person." theory is sound. It's kind of like how the games talk about the deeds of the player character in the main quest, but are vague as to details like the character's race, six, class and such.
This is not a disagreenent with you, if someone knows how these events unfolded in lore pleas correct me.
Just that the events in tribunial, where very political and involving Beneziah who is a central elder scroll figure and her family. So as has been put in the past the events in Mournhold would I think be from her and her sons point of view.
Bloodmoon I would say the Neverarine may get mentioned, but again the company and legion are more likely to spin one story. and the Nordic inhabitants another.
If we take Dive rock, I am sure the note mentions a hero, but not a specifc hero. So if we take that for granted, which I am loathe to do the Neverarine if truely the hero of solstheim did so incognito.