No, it didn't. If it was US territory, then any Kraut born there would be a US citizen by way of the 14th. Since that's not the case, it wasn't US territory in any relevant legal sense.
We had to travel to the US Consulate in Munich to get their US Birth certificate
Which would not have been necessary, had the Army hospital been US territory, would it? In any case, it was a mere formality to ratify the fact that your kids were citizens from birth and hence eligible to run upon attaining the age of 35.
Don't you tell me what my husband had to or not had to do. You obviously had never served in the military and been stationed overseas with your family, otherwise you would know what I am saying the truth.
If they had been born in a civilian German hospital, that would have been a different story, but they were not. I am sure there are freepers who have served and been stationed overseas with their families and have children that were born overseas can confirm what I am saying and they also had to go to the American Consulate for the birth certificate.