If the Founders were following Vattel, they should have followed his phrasing and used "native citizen" rather than confusing everyone by using a term so close to the common law phrase "natural born subject".
But they didn't, and the phrase they used makes sense as the American version of Natural Born Subject.
"II. The fundamental principle of the common law with regard to English nationality was birth within the allegiance, also called "ligealty," "obedience," "faith," or "power" of the King. The principle embraced all persons born within the King's allegiance and subject to his protection. Such allegiance and protection were mutual -- as expressed in the maxim protectio trahit subjectionem, et subjectio protectionem -- and were not restricted to natural-born subjects and naturalized subjects, or to those who had taken an oath of allegiance, but were predicable of aliens in amity so long as they were within the kingdom. Children, born in England, of such aliens were therefore natural-born subjects. "
They also cite Dicey:
"Natural-born British subject" means a British subject who has become a British subject at the moment of his birth." and "Subject to the exceptions hereinafter mentioned, any person who (whatever the nationality of his parents) is born within the British dominions is a natural-born British subject. This rule contains the leading principle of English law on the subject of British nationality."
There's nothing confusing about the terminology, other than your refusal to admit what the words actually say. All children, born in the country of parents who are citizens = the nomenclature familiar to the founders. These are the natives or natural born citizens. So simple, even an obot should an understand.
But they didn't, and the phrase they used makes sense as the American version of Natural Born Subject.
Except that nothing in the decision ever says that natural born citizen is the American version of natural born subject. They were specific in the words they did use. Plus, we know U.S. law rejected at least one or more of the unnatural constructs of natural born subjectship. Children born overseas weren't inherently considered to be natural born citizens. It took a naturalization act to express this principle, although it was short-lived. So much for that faither theory.
They also cite Dicey:
It's funny how you faithers go on and on that Vattel isn't U.S. law, but you have no problems citing other names and acting as if those are, despite the fact that, for example, Dicey's definition was not cited as THE definition of natural born citizen, while Vattel's was. Ouch, faithers, ouch! Further, this 'leading principle' of English law was enacted through a naturalization declaration by a king who was unilaterally claiming the subjects of Scotland as his own. The act didn't pertain to foreigners, per se, but to Scots whose children were born in England.