Not so.
A US installation overseas is nt US territory.
McCain was born on American soil - the Panama Canal Zone.
Korea is not US soil. Citizenship at overseas bases derives from the citizenship of the American parents.
My son was born in a military hospital. He was issued a Department of State ConsularReport of Birth Abroad of a and is a US citizen and citizen of North Carolina.
The part about US Soil is that every flag pole is sunk in soil from the United States, symbolizing our sovereignty at that post; you are correct that it is not US Soil for citizenship....
Or, like McCain, off the US military base in a civilian hospital? - McCain was derived from his parent being in the military, for which their are stipulations in law to address concerning citizenship, separate but overlapping the similar stipulations for "born of two US citizen parents".
A Consular Report of Birth Abroad may be issued for any U.S. citizen child under the age of 18 who was born abroad and who acquired U.S. citizenship at birth. Only the child's parent(s), legal guardian, person acting in loco parent is or the child may apply on the child's behalf. The application generally must be signed before a U.S. consular officer, a consular agent, or, in the case of children born in U.S. military hospitals, a designated military official. A Consular Report of Birth Abroad is proof of U.S. citizenship; however, and does not take the place of a passport for travel purposes.