Not by statutory or codified law, but by practice and misapplication. The 14th Amendment, for instance, does not establish automatic citizenship on an "anchor baby," because that baby is not subject to the jurisdiction of the United States, but is subject to the jurisdiction of the country of which his parents are citizens. Politicians and jurists with agendas interpret laws to reflect their own biases. That's why the lefties torture the clear and unambiguous meaning of the 2nd Amendment's "...the right of the People to keep and bear arms, shall not be infringed," (an independent clause), and try to make it dependent on (the dependent clause) "A well regulated militia;" and why they misinterpret the 18th century "well regulated" to mean "well controlled," and not the "well-functioning" that was clearly intended.
I happen to agree with that but it does not change the fact that "the law" says they are citizens by birth and thus if a citizen by birth is the same as a natural born citizen then whether you like it or not, under your definition of an NBC that Chinese kid is an NBC and eligible to serve as POTUS.