Why do people think this and what proves it?

There's no official canon on it, it's just open to interpretation.

But why do people think this, and what proves it?

What evidence, actions, or events would suggest that? What leads people to that conclusion?

In the recorded lore following the event in Oblivion, it is assumed that the same protagonist who completed the main quest, also completed the Shivering Isles expansion of said game.

Therefore, the same being who purged Kvatch of Daedric filth also traveled through the strange door in Niben Bay. Far along in the Shivering Isles questline, Sheogorath the Madgod is no more. Jyggalag, the Daedric Prince of Order, appears in his stead; the Greymarch is fully complete at this time. After the player destroys Jyggalag outside in the Courtyard of New Sheoth's Palace district, the player effectively breaks the eternal cycle of the Greymarch and becomes the undisputed ruler of the Shivering Isles, cementing his/her status as Madgod.

It is a bit confusing, but it is true.

Perhaps I should look more into the Shivering Isles for further reading then.