“when they are born a U.S. citizen they are not ‘naturalized’.”
They are made a citizen, just as a naturalized citizen is made a citizen. Since they are made citizens, they could not have been citizens before they were made citizens. Otherwise there would have been no reason to have a law, commnlaw or statutory law, to make the person a citizen at birth or subsequent to birth in the event they had been a citizen at birth without such a law.
A true natural born citizen is a citizen without the action of a jus soli or jus sanguinis law to make them a citizen at birth or subsequent to birth.
A person who is made a citizen at birth by act of a law as if they are naturalized at birth is by the action of law an unnatural citizen at birth and not a natural citizen at birth.!
A natural born citizen is one who through EITHER natural law concepts of jus soli or jus sanguinis and according to the natural law concept of “under the jurisdiction thereof” - is a citizen at birth.
Now you invent the concept of an “unnnatural citizen at birth” - unrecognized in U.S. law - or English law - or Vattel - and completely at odds with natural law.
One either has allegiance at birth through natural law or not. This natural allegiance at birth is recognized by granting the child citizenship at birth.
In the USA one is either born a citizen or one must be naturalized as a citizen. Being born a citizen in recognition of natural law concepts makes one a “natural born citizen”.
So where and by who is “natural born” defined such that McCain would not be eligible?