To me the killer was when Kenya announced that they had sealed his records. If they have anything to seal, then O'bummer cannot be a US citizen.
They know the hospital and have three affidavits by people who say they were there when he was born in. They know the name of the hospital, doctor etc. Apparently Sidney Ann was too far into her pregnancy to travel. She had the baby in Africa, registered him in HI upon her return. (Remember she was still a minor when this all happened.)