No, it’s the opposite. In this case, everyone agreed that the “and” means both conditions must hold. Everyone agrees that someone must be both (1) born in the US and (2) subject to the jurisdiction of the U.S.

Under your reading, the whole discussion about children of diplomats makes no sense. Under your reading, children of diplomats would automatically be U.S. citizens if born on U.S. soil. But everyone agrees that they’re not.