British law matters if they are making the argument that his British citizenship disqualifies him even if born on US soil.
But I don't accept that argument. Rather I think that it is the lack of US citizenship of his father that matters, not his, or his father's, British citizenship. If that is, BHO Sr. was his legal father and married to Stanley Ann. My conclusions are no different, but the path to them is, and the path has the "advantage" of not depending on any foreign law.