A logical point. To take the logic further, why would the Founders use the Law of Nations internally, yet ignore its use internally?
The answer is, of course, they wouldn't.
Vattel's idea that 'natives, or natural-born citizens, are those born in the country, of parents who are citizens' was repeated decades later in Congress-
“[I] find no fault with the introductory clause, which is simply declaratory of what is written in the Constitution, that every human being born within the jurisdiction of the United States of parents not owing allegiance to any foreign sovereignty is, in the language of your Constitution itself, a natural born citizen. . . . ”
— John A. Bingham, (R-Ohio) US Congressman, March 9, 1866 Cong. Globe, 39th, 1st Sess., 1291 (1866), Sec. 1992 of U.S. Revised Statutes (1866).
-----
because it would be incredibly stupid - is that a translation made in 1797 determines the meaning of a phrase written in 1787.
A Subject of the King was subject to the King's whims where a Citizen is his own King.....it's why we're 'Sovereign' citizens.
It can't be that that hard of a stretch to see that a subject in Vattel's work is analogous to Citizen to the Founders.