If your parent/parents served in the military, and you were born overseas, how could you acquire your birth certificate?
Birth on US Military Base or Facility
People born on a United States military facility outside of the United States should contact:
American Citizens Born Abroad
Department of State
1111 19th Street NW
Washington, DC 20522
People born on United States military facilities within a US State should contact the State office of Vital Records for the state the facility is in.
You could also request your birth certificate from your sponsor’s medical record.
This is the section of US Law that defines "Citizen at Birth", which is currently the legal definition of what "natural-born citizen" means:
A person needs to satisfy only one of the conditions listed there to be considered a citizen at birth.
Note that US Military bases are NOT considered US territory, though US Embassies (but not Consulates) ARE.
The Panama Canal Zone was explicitly included (by a US Law passed by Congress) to be "sovereign US soil".
To answer the question: being born on a foreign US military base is no different than being born in a foreign country, for determination of US Citizenship at Birth. Neither qualify. It would depend on the person's parents to determine eligibility for Citizenship at Birth.