It’s been proved to be a fake and I don’t buy what you are saying.
Unfortunately for our side, few people know there are TWO sets of BC photos going around - one badly and obviously faked, the other accurate as far as any expert can attest.
(Are you even looking at the links I'm giving you? only takes a few seconds.)
Now, given the circumstantial evidence coupled with BHO's extraordinary efforts to keep the original sealed, I'm with you in believing that he is in fact disqualified* - we just don't have the legal evidence to prove it.
(* - my take is his mother tried to fly to Hawaii before the birth, the airline wouldn't take her for risk of on-plane delivery, and she flew with him to HI after his birth in time to have a falsified "at home" BC registered within 3 days of delivery. There is evidence, but he has it sealed away, and what has been produced (argued above) is legally binding just like a passport acquired on false pretences.)