And unfortunately for you - American law prevails for those born in America. They can exercise their British citizenship - but in situations where you have dual citizenship - the American law prevails. Every time.
There is no need for American law to "prevail" as those born subject to another country's nationality law are not birthright citizens per the 14th Amendment as written and intended.
The Supreme Court has loosened the 14th Amendment's requirements somewhat in ruling that children born in the U.S. to parents who were permanently domiciled in the U.S. at the time of the child's birth also confers birthright citizenship. - U.S. v. Wong Kim Ark
Those born in the U.S. to a temporary resident alien are not legally born U.S. citizens at all, let alone natural born citizens.