Your not saying an American can go get Mexican citizenship, and then run for US president and qualify as a NBC?
Why not?
If that were not the case, any third-world country that chose to do so could award citizenship to any of our politicians and thereby make them ineligible for president.
I’m not saying I would approve of any such action or vote for such a person, but I don’t see any legal or constitutional bar.
Our legal system does not presently recognize dual (or more) citizenship. Whether they also hold citizenship from another country is just not relevant to a person’s status as a citizen in this one.
I’m referring, of course, to whether a person who is an American citien subsequently acquires citizenship with another country. I’m well aware those who become naturalized are required to forswear allegiance to other countries. But even there we make absolutely no effort to track down whether a newly naturalized American from Venezuela has been removed from the Venezuelan citizenship rolls. Status as a Venezuelan citizen is irrelevant to American citizenship.
You may believe a person should lose NBC status if they obtain citizenship in another country, and I would probably agree with you, but I know of nothing in the Constitution or laws that implements it.