In your mind then the Founders equated being a subject of the king with being a citizen of a republic? The history of the founding is completely to the contrary. Jefferson, for example, in his drafting, specifically rejected the word “subject” and replaced it with “citizen.”
Not in my mind. I cited the Court's opinion in Wong Kim Ark, where Justice Gray clearly stated 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."
I have Supreme Court jurisprudence on my side. Do you? Even in Minor v. Happersett, Chief Justice Waite resorted to common law to define "natural-born citizen"; he did not cite de Vattel at all in the Court's opinion, which was unanimous and accompanied by no concurring or separate opinion.