The law assumes the child is NOT a citizen of the US. Else there'd be no need to add the child to a visa since US citizens don't need a visa to be inside the US.
Foreign rules regarding Americans who give birth abroad are comparable.
There are also "status of forces" agreements in many countries and military personnel may be governed differently (regarding the visa deal).
Just quickly looking through the State Department's rules, it doesn't say children have to have a passport (when accompanied by a parent or guardian).
Yes they do. "All Children regardless of age (including newborns and infants ) must have their own passport".
But in 1961, a FReeper pointed out that the rules were different.