If you are going to cite Vattel as the authority, notice that Vattel specifically exempts a nation's fighting men from the jus soli requirement.
Thank you thank you thank you!
That’s not what they taught us Marine Corps Brats, in a school on the base, being taught by teachers hired by and supervised by the Marines. We were told explicitly that this meant those of us born overseas couldn’t hold the Office of the President.
Oh for a time machine...