Hawaii Revised Statute 338-17.8 allows registration of birth in Hawaii for a child that was born outside of Hawaii to parents who, for a year preceding the childs birth, claimed Hawaii as their place of residence. The parents would be issued a Certification of Live Birth. This is not proof of where the child was born. It only proves that the parents claimed Hawaii as their main place of residence for the prior year.
British Nationality Act of 1948 (Part II, Section 5): Subject to the provisions of this section, a person born after the commencement of this Act shall be a citizen of the United Kingdom and Colonies by descent if his father is a citizen of the United Kingdom and Colonies at the time of the birth.
A natural born citizen, would not be a citizen of any other nation than the United States. That is what "natural born" means. By nature, the child, would be only a US citizen, because both of his parents were US citizens, and NO OTHER NATION, can by law claim him to be under their jurisdiction, at the moment of his birth. That was not the case with Obama. He was, by law, a Citizen of the United Kingdom, the moment he was born, and then, by law, he became a citizen of Kenya on Dec. 12, 1963.