I believe Mitt Romney was born in Mexico
Could you be thinking of his father Governor George Romney ?
Yeah, I got them mixed up. But the principle is the same. George Romney was born in Mexico of American missionary parents, yet was a candidate for the presidency and, as far as I know, was considered a natural born citizen.
Hawaii offered this certificate of live birth because there were so many births at home and away from Hawaii in the early years of statehood. It is dependent on facts given to the registrar and does NOT constitute Citizenship, just recognizes birth.