Not sure about that. My friend had her daughter in Germany while hubby was stationed there. The daughter has dual citizenship.
Germany may offer the child citizenship, but as a child born overseas to a family on official duty, she is a native born natural US citizen.
The US does not recognize duality. Either you are a US citizen or you are not.
It also depends on where the child was born- if in a US military hospital on US installation, then Germany has no record of her birth, if in a German facility attended by a German physician, then she indeed may have a German BC, but that BC will specify the citizenship of her parents. If the latter, the parents needed to file ( the hospital probably did I while they were there) a form to the US Embassy reporting the “birth of a US Child abroad”, beginning the US State issuance of a BC.
My son was born in a similar situation, but in a US facility, he searched the German records for any reference to his birth in West Germany, there is none. He is a US citizen naturally, by virtue of our official duty there. He has a US State Department BC.
This puzzles me too. I married an English woman while stationed in London. We had two children there and I know for a fact that they can claim British citizenship as well as American. I’m not sure if they can be considered natural born U.S. citizens though; I think not. Sure would be nice to have this mess cleared up once and for all. i.e., is Ted Cruz eligible to become President? Are my daughters?