No, but allegiance to other countries prevents it and the allegiance is determined by the country to whom the father or mother is a citizen off. With China and Britain it was different then with other countries because citizens were considered subjects.
Listen, if you want to argue go stand in the corner. If you want to really learn about this, go research it.
So, following your logic, a foreign country (such as North Korea) could have disqualified George Bush from the Presidency by passing a law making Barbara Bush a citizen of that country? That's the logical extension of your argument, if the parents' citizenship can disqualify someone born in the US from the Presidency.
With China and Britain it was different then with other countries because citizens were considered subjects.
So what?