I would think that the father's name on the long form birth certificate would establish parentage, married or not. The Certificate of Live Birth form, in '61, did not even contain a field to indicate if the parents were married. It also asks for the mother's maiden name, not her married name, if any.
Thus, if the test for NBC is having two US citizen parents, he fails, IF the long Form BC shows BHO Sr as his father.
IMHO, the search for British citizenship for Junior is misplaced. It doesn't matter. Citizenship of his father, the legal one, does. If the father was not a US Citizen, the child is not an NBC. Now there are potential circumstances that would make BHO Jr. not even a citizen, unless later naturalized, but confirming those could prove difficult.
Father’s citizenship was crucial to the founding fathers. Otherwise why did Chester A Arthur spend so much effort covering up his father’s foreign birth?
Is in not interesting that father’s provenance had more weight than mother’s. Women did not have the vote either...And it should have stayed that way (LOL)