That makes no sense. Re-read what you just wrote.
How can Natives=Mexicans, but Natives got Anglicanized and Mexicans got Spanishized- which isn't even a word btw?
There are several different tribes that roamed the Americas before European settlers. The most prominent being Incas, Myans, Caribs, Arawaks/Tianos, Seminoles, Cherokees, Capachees. Most of the members of these tribes died off and the remaining few mixed with the Europeans.
That makes their descendants mixed race or mezitos.
Some have a higher percentage of Euro DNA other have a higher percentage of Native DNA, the descendants from tribes in the US more than likely have very little Native DNA.
A Mexican referring to themselves as Native American would be the equivalent to an African American referring to themselves as African or Nigerican, or a person from DR referring to themselves as Tiano.