So naturally someone born in a stable must be a horse.
Reducto ad absurdum.
If the stable was in the US or its territories, then the person is a US citizen by birth. If that stable was in Bethlehem, then the child born is a citizen of Israel - not the US.
Here's a direct, simple question for you: do you gain citizenship by being born on US soil? Simple yes or no answer is all that is required.