It's actually so stupid that Tulius couldn't give less of a fuck about the MC being the DB. Tulius is a seasoned strategist. Anyone in either his or Ulfric's position would immediately go "holy shit this person is a symbol of myth to the people and wants to support me. This is my hail mary"

I guarantee you it was streamlined out because Bethesda just works like that. Most fantasy stories that came before it have capitalized divine heros perfectly fine. But Skyrim is just you're both the most important person on Tamriel but also not different than your average joe.