You're almost understanding. Those persons you are describing are NBCs. If the so-called "ancient and fundamental rule of citizenship by birth within the territory" was so ancient and fundamental, then why is there doubt about those who are NOT born to citizens?? The answer: they are not NATURAL-BORN citizens. The ancient and fundamental rule comes with strings and doubts, but only one class within this rule has no doubt: those born in the country to citizen parents, i.e., Natural-born Citizens.
All persons born in the allegiance of the king are natural-born subjects, and all persons born in the allegiance of the United States are natural-born citizens. Birth and allegiance go together. Such is the rule of the common law, and it is the common law of this country, as well as of England. We find no warrant for the opinion that this great principle of the common law has ever been changed in the United States. It has always obtained here with the same vigor, and subject only to the same exceptions, since as before the Revolution.
But,but,but,but(you'll say). . .ALL persons just can't mean the aliens and foreigners!!! YES IT DOES. The court says:
It thus clearly appears that by the law of England for the last three centuries, beginning before the settlement of this country, and continuing to the present day, aliens, while residing in the dominions possessed by the crown of England, were within the allegiance, the obedience, the faith or loyalty, the protection, the power, and the jurisdiction of the English sovereign; and therefore every child born in England of alien parents was a natural-born subject, unless the child of an ambassador or other diplomatic agent of a foreign state, or of an alien enemy in hostile occupation of the place where the child was born.
III. 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.13
Sooo, it is time for YOU to break out of the Vattle Cult, and quit being a Vattle Birther. This is as close to doing it as YOU will probably ever get. If you don't, you will end up like the Moon Landing Deniers, spending your life spouting off a bunch of cult nonsense and having people either ignore you as a nut, or poke fun at you. I hope you do the right thing.