THe “Natural born” part of “natural born citizen” primarily deals with WHERE someone is born. Being born on the soil of the country makes you “natural born”.
It’s the “citizen” that depends on the law. Or, because we love laws, we actually wrote a law which tries to confer “natural-born” on people who were not actually “natural born”, because they were born on foreign soil, not “natural” soil. But that’s why those laws exist, because they are trying to change the definition of “natural born”.
So you are wrong to suggest that a person born on US soil could be a “citizen” but not a “natural born” citizen. In fact, the opposite is true, they could be “natural born” but not be a citizen.
Except that current law says anybody born on US soil except for specifically named special cases (like ambassadors) are citizens.
The law of nations spells it out for you.
Yhat’s the document the fouding fathers used.