You are reading it incorrectly. George Romney was born a US citizen with allegiance exclusively to the US because of the law of nations & treaty with Mexico, the Mexican government did NOT recognize him as one of their own. He was born a foreign national to Mexico even though the event took place on Mexican soil. If the US had denied him citizenship, the he would have been left stateless.
Being a refugee does not take away your citizenship. Under the laws of nations, whatever citizenship you take with you when you travel outside the nation is your citizenship until you attain another. That is why immigrants were/are discouraged from traveling to the countries of their birth citizenship until their US citizenship process is complete. Until it is complete, those immigrants still remain under the jurisdiction of the foreign government. This was never the case for George Romney. Mexico never laid claim to him. He was exclusively a US citizen from birth.
Just because the article claims Romney is not Mexican
does not mean it is true.
Bishop Romney is not eligible.