“According to your theory, all China would have to do is issue citizenship to every American born and then no one can be President.”
Only if the US recognized the citizenship - which it obviously does not.
Obama’s legal documented (regardless of actual) father at birth was a British subject.
Like the PM of Thailand - he is a dual citizen to this day.
Not exactly the intent of the founders.
My sister was born in England and her father was a military serviceman. She holds US recognized dual citizenship. She is also a natural born citizen, by law and by the First Congress’s definition, regardless of the fact that England grants her citizenship.