My sister was born in Tokyo in 1954. Because she was not born in the army hospital, she held dual citizenship until she was 21. Sounds cool. But it was a pain in the ass the first time she needed to prove citizenship for her passport. For some reason the would not accept her army paperwork, so she had to get docs from the Japanese Embassy.
It can get crazy. I personally know of one case where an unaccompanied wife of an enlisted guy had a child born at Landstuhl. Because she was under 18, the consulate at Frankfurt would not give her a passport for the child. The law was so worded that her congressman had to get a private bill pass which identified her as an American citizen. Because she was not on his orders, she did not fall under the SOFA. His commander went to bat for him,went all the way to headquarters and got new orders cuts for him. But that was after the private bill passed.