“One must be born on USA soil or its military bases.”
Birth on U.S. military bases, embassies, and consulates does not constitute birth in a U.S. jurisdiction. This is described in the U.S. State Department Foreign Affairs manual in regard to the acquisition of U.S. citizenship by a child born abroad with a U.S. citizen parent. It also describes how such children are U.S. citizens naturalized at birth and are not natural born citizens.
You again are confused. The issue is not citizenship alone. It is citizenship plus being born here = Natural born citizen. Not just “citizen”— “ Natural born citizen”. Almost 34% of Americans now think Cruz was not “natural Born”. It is a major issue. it is eligibility to be president under the strict rule that no foreign born individual will ever be president.