I think, at the time he was born, it was different than it is now. So there are people who insist he fits the criteria as it is now. Something about his mother, while a citizen, was not old enough to convey citizenship to BO based on her status. I don’t remember the exact details. Also a later question (sort of related) that he likely became a citizen of Indonesia when he moved there, that Indonesia does not or did not allow dual citizenship, and he never changed his citizenship after his time living in Indonesia, so he may NOT be a citizen based on those issues.
NBC is a class of it’s own. Before the term was used in our Constitution it is found in de Vattel’s Law of Nations. Unfortunatley, the Supreme Court also refers to Blackstone’s English Common Law, England had subjects, not citizens.
George Mason of Virginia stated at the Constitutional Convention that “The Common Law of England is NOT the Common Law of these States”.