One thing to consider is that indisputably you do indeed walk out of the Shivering Isles decked to the nines with new and powerful weapons, so at least something tangible did, indeed, happen there.
I'm not imagining my full madness armor or sword of jyggalag.
Or are you really out of that door? How can you be 100% sure that your eyes have not deceived you. In a land of complete madness, do you not find it strange that you are the only sane one roaming around? And yet, you were pronounced the Madgod at the end. It may actually be that you are running around naked, with a can on your head, and you are imagining everything. Oh, and those monsters and dungeons you are beating? Those may just be household items you are breaking, and you are actually inside your home. And the door leading back to Nirn could just be the door outside.
Remember, this is Sheogorath's land. You could just be completely delusional and this whole thing is a giant illusion.
EDIT: The only thing I can definitively say is that the CoC is completely out of the picture, and we may not know of his/her existence until the next game, or a dev comes along and tells us. Jyggy ends up with his own shrine, we can take what happened in SI with face value. If rumors appear that the CoC went inside some strange door and never came out, and there are no jyggy shrines, it could still be thought he is stark raving mad in SI, or he is the Madgod, and Jyggy just doesn't have a shrine yet.
EDIT2: Also, is that little passage about the Kajiit or something who partly defiled the CoC's statue, is that considered canon? I forgot the other details, other than that part. I think the statue was graffiti with the words "Skooma Cat"