Have I got that right, Nully?
Merely being an American citizen did not suffice, they reserved the office to that singular person, a "Natural Born Citizen", someone of undivided loyalties based on BOTH place of birth AND citizenship of parents.
Thus they followed both Vattel and Blackstone in believing that a Natural Born Citizen is a citizen both under the doctrine of jus soli, that is by being born on the soil of the country, and jus sanguinis, by having the blood of that country's citizen parents flowing through their veins.