Actually, the origin of the phrase natural born comes from Law of Nations. It requires that the person be born here, to two parents who are citizens, and that no foreign power has claim to them. In Obama’s case, the birthplace is only one obstacle. Even if he is proven to have been born in Hawaii, his father was a British citizen AND British law claims the child of a British father as a British citizen.
Good thing we're not governed by British law and our citizenship status doesn't change depending on what some foreign country says.