Your right, British law doesn't determine US citizenship.
However, you omit the opposite question.
Does US law determine British citizenship? The answer is equally no. Therefore, his admitted British citizenship AT birth is most relavent.
In Britain.
It's a simple principle: Citizenship status, including "natural-born" status, is a question of US law. Full stop. The laws of other countries are irrelevant. We don't ask whether the Republic of Panama considered John McCain to be a Panamanian citizen, and we don't give other countries the power to make someone ineligible to be our president by the stroke of a pen.