Your opinion and the opinion of the Supreme Court are not in agreement.
The Supreme Court of the United States has never applied the term 'natural born citizen' to any other category than 'those born in the country of parents who are citizens thereof'.
The Most famous case regarding this issue is Wong Kim Ark.
Do you know what the Supreme court said in Wong Kim Ark?
Every person born in the United States, and subject to the jurisdiction thereof, becomes at once a citizen of the United States, and needs no naturalization. A person born out of the jurisdiction of the United States can only become a citizen by being naturalized, either by treaty, as in the case of the annexation of foreign territory, or by authority of Congress, exercised either by declaring certain classes of persons to be citizens, as in the enactments conferring citizenship upon foreign-born children of citizens, or by enabling foreigners individually to become citizens by proceedings in the judicial tribunals, as in the ordinary provisions of the naturalization acts.