Plus I think you got brownie points for being born in a US Army hospital to real American parents. I am assuming that one parent was in the Army?
That actually doesn't make a difference. Embassies and military bases aren't US territory- that's mostly an urban myth. Rather, they're places where the host country has agreed, by treaty, to let the US exercise its jurisdiction. Imagine a situation where a pregnant German woman went into labor on a US base in that country and was rushed to the base hospital because the delivery was imminent. Unless the father was a US citizen, that child would not be a US citizen under any circumstance.