There was no US common law in 1787 which would define the meaning of legal terms as understood in 1787. It was ENGLISH common law that formed the language of the law.
I have seen over and over a distinction made in period writings. So, just WHEN was common law integrated into American law, and just WHEN did we cease using English law? According to you?
And wouldn't you know the English Common Law book which defined "natural born subject" used the Vattel Definition?
This was from John Adam's own personal copy of English law, by the way.