Incorrect.
The rules of naturalization define who is a citizen at birth and as such, define those who are naturally born as US citizens.
The book “Laws of nations” has no authority under the US Constitution which is the supreme law of this nation. As such, only CONGRESS has the enumerated power to set the rules of who does and who does not need to be naturalized.
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.
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It was repealed, with George Washington specifically having that line expunged, and the act was replaced with the words now absent.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.