Other highly esteemed legal authorities of the time who stated that the phrase in question was taken from the law of nations and Vattel were St. George Tucker and Daniel Ramsay. These were all men who fought in the Revolution and knew the Framers. Tucker edited the most prominent American edition of Blackstone and at the end of his addition added notes pointing out where the Constitution varied from Enlglish common law and looked to the law of nations. Luther Martin of Maryland, during the constitutional convention, read so extensively out loud from Vattel, along with Locke and others whose works were a great influence upon the drafting, that the others grew impatient with him.
Then there is the well known letter of John Jay, who had been bi-lingual in French from his early years that led to the choice of the phrase. In short there is much evidence that the Framers followed the law of nations in matters concerning cirizenship as Story held and there is no specific evidence to the contrary, only vague statements that the Framers were familiar with English common law, without a single example that shows that they specifically followed it in matters of citizenship.
Thus, what you say seems very poorly informed and unsupported by history and legal authority.
What I say comes from the Supreme Court. You can't support your argument better than that.
In Wong Kim Ark, Justice Gray used the phrase "natural-born subject" over twenty times and did not once cite de Vattel. Instead, he performed a thorough analysis of English common law and concluded that "The same rule was in force in all the English Colonies upon this continent down to the time of the Declaration of Independence, and in the United States afterwards, and continued to prevail under the Constitution as originally established."
Moreover, in Minor, Chief Justice Waite resorted to (English) common law to define "natural-born subject," and he also did not cite de Vattel anywhere in the Court's opinion, which was unanimous.
The problem is simple: "natural-born citizen" isn't defined in the Constitution, and there is more than one definition of "natural-born citizen." On the one hand, you have the well-established definition of "natural-born subject" from English common law applied to "natural-born citizen." On the other hand, you have a specific French-to-English translation of a Swiss legalist's writings. Which would a reasonable person in 1788 have used to define "natural-born citizen"?
In two Supreme Court cases, Minor and Wong Kim Ark, the Court looked to English common law to define the phrase, not de Vattel. In Wong Kim Ark, the DISSENTERS cited de Vattel once; thus, they failed to convince the other six Justices that de Vattel's definition was used over English common law's.