Until 1783, the colonists were "natural-born subjects" of the British Crown, and the phrase "natural-born subject" was well-defined in English common law. Moreover, the phrase really was "natural-born subject" in the English language; it was not a specific translation of four French words written by a Swiss legalist.
You're saying that a reasonable person in 1788 would've used de Vattel's definition because in your opinion, de Vattel's definition is more "natural" (literally--no pun intended). It may very well be more "natural" to you, but it remains that "natural-born subject" as a legal concept existed and was well-defined in English common law. The two definitions differ, so which would a reasonable person in 1788 have used?
Given that a reasonable person in 1788 had been a "natural-born subject" of the British Crown a mere five years earlier, I argue that he would use the English common law definition of "natural-born subject" applied to "natural-born citizen." About a century later, in Minor, Chief Justice Waite recognized that the Constitution doesn't define "natural-born citizen" and hence, resort must had "elsewhere" to define it. Chief Justice Waite immediately looked to (English) common law; he did not cite de Vattel at all in the Court's opinion, which was unanimous.
The Founders didn't define "natural-born citizen" in the Constitution. No one doubts this. Quite a few of you, however, insist that if it isn't defined, we must consult the English translation of a book written by a Swiss legalist in French. Uh, why? Why not consult English common law, which actually has a phrase that would be identical if not for our lack of a monarchic system?
The impunity with which the disloyalty of today is rewarded is one reason the people of today lack the commonsense to understand the starkly simple linkage between loyalty, allegiance, and citizenship.