A US military installation (even a ship) is US territory. I think the only problem with McCain was that he was born in a hospital that was outside of the base. I don’t believe the base had a maternity facility, or something like that.
A friend of mine, now a retired colonel, was born in a British Army facility to a U.S. Military father and mother stationed under orders at that facility. There was never a question about his being a native born citizen. The difference between McCain and BO is that he was born in another country to parents who were American born and who were there under government (military) orders.