The point is that “natural born” (the English term) did not come from Vattel. The term “natural born” in fact was taken from English common law, as the post and the link clearly state.
That the term “natural born” was used at all indicates that they were using a term known to them from English common law. Were they to have used Vattel as their intended meaning and been intelligent fellows, the LAST thing they would do is use a term that was so obviously taken from English common law.
That you all cannot see this is a choice you have made to be intellectually dishonest. Either that or you’re just stupid.
The Constitution specifically refers to The Law Of Nations, capitalized as a proper noun. As there is only one such book, it serves as the ONLY reference material on the subject. Later court decisions have been quite explicit in referring to this specific text, not to a general “law of nations”(lower case).
Checkmate.