A naturalized citizen who was born on American soil to an American mother? The Constitution is very clear that such a person is a citizen at birth, so there would be no reason for naturalization.
By virtue of his father being a British subject he would have dual-citizenship. As you recognized yourself the choice to retain U.S. citizenship exists making it self-evident that the person in question is only a U.S. citizen by naturalization. A “natural-born” citizen never has to make a choice or take any action to secure his citizenship status.