They didn't consider themselves to be natural-born subjects which was perpetual. We know this from James Madison. He said that the local community came ahead of the crown ... that persons were primarily citizens of the colony in which they were born AHEAD of being subjects of the crown.
What was the allegiance as a citizen of South-Carolina, he owed to the King of Great Britain? He owed his allegiance to him as a King of that society to which, as a society he owed his primary allegiance. When that society separated from Great Britain, he was bound by that act and his allegiance transferred to that society, or the sovereign which that society should set up, because it was through his membership of the society of South-Carolina, that he owed allegiance to Great Britain.
The Shanks v. Dupont decision echoes this principle:
On that day, Mrs. Shanks was found under allegiance to the State of South Carolina as a natural born citizen to a community ...
- - -
Upon the whole I am of opinion that Mrs. Shanks continued, as she was born, a citizen of South Carolina, and of course unprotected by the British treaty.
The founders - by force of arms - freed themselves from being subjects and founded a government where the citizen was sovereign.
But prior to the Revolution - they were subjects - and subject to the laws of England - and born as “natural born subjects” of England.
My point is that there is or was NOTHING in English law to differentiate those born as subjects of England and those who were natural born subjects of England.
To be born a subject of England was to be a natural born subject of England.