Not so fast, A. I would not put it past this president to go to court and claim since there is no proof of his long form BC, you can't prove BHOI WAS his father, therefore you can't prove he ISN'T eligible. And it is the essence of US American Democracy that one is innocent until proven guilty.
The innocent till proven guilty is not immediately at issue since this is not yet a criminal issue but a qualification issue which must abide by court orders.
Not that I would not expect Urkel’s minions would try it.