You can orbit at any altitude in a thought experiment, which is what this is. Nitpicking about the irrelevant parameters of the thought experiment is just dodging the question. For those of you who simply cannot get beyond forcing an idea into a real world scenario, just think of it as a plane flying over the country in route to another country.
There is nothing intrinsic about being in national airspace that would confer citizenship on a child born in an airplane, either. For instance, if it were an Air France flight, the interior of the aircraft would be French territory. The woman wouldn't enter the US until she landed there and cleared customs.