The founding fathers themselves used the book as an "authority" when writing the constitution! When they use the term "natural born citizen," it is taken from Vattel. It is their original intent. And as long as that is true, the assertions of modern day litigators (who also tell us anchor babies are citizens)-- with no grounds to make such a claim-- cannot stand.
Further, the very first act of Congress, the Naturalization Act of 1790 set the precedence that being born on US soil is NOT a requirement for citizenship at birth.
It was repealed, with George Washington specifically having that line expunged, and the act was replaced with the words now absent. It would have been considered unconstitutional.
It was repealed AND replaced.
As was the law that repealed and replaced it.
And so on and so forth until you get to the current law as expressed in Title 8 section 1401.