I cheerfully agree that the term is not defined.
I do find your position above somewhat odd. It implies that a person born of American parents is somehow more loyal to America as a consequence.
While this may have been a reasonable provision for the Founders to stick in, it is pretty obviously not a fact in today's world.
We have many millions of perfectly NB citizens who are enthusiastically anti-American. And millions of pro-American naturalized citizens.
Just pointing out that the Founders could not have envisioned a culture in which the majority of the ruling elite would be anti-American.
Sad but true.