“Yes, that is true, BUT “
There is no “BUT” ... you are confusing a basic and simple term of art with the legal satisfaction and requirements for that term.
“natural-born citizen” means ‘citizen at time of birth’.
Any arugments over who is a natural-born citizen are arguments over who gets to be a citizen at time of birth.
A person born within the jurisdiction of a national government” is either a citizen or subject at time of birth.
There is a 'BUT' alright. That you did not understand or ignored the word "jurisdiction" in Black's Law Dictionary ...you likely did not understand the word. No 'term of art' nonsense.
I enlighten you faither to the meaning of 'jurisdiction.' Here again,
"..."Jurisdiction" is not only "territorial jurisdiction" but it encompasses allegiance owing jurisdiction where the foreign citizen who owes allegiance to a foreign sovereign. A foreign citizen can pass on their foreign sovereign to their child born on a foreign land, therefore, the child is NOT a natural born citizen. "
Black's Law Dictionary definition is no different than Bouvier's Law Dictionary as seen below.
As we see, Bouvier's Law Dictionary informs us to the meaning of the word "jurisdiction" in their definition while Black's Law Dictionary does not.