Origins

Picky, picky, picky. The term American Indian is a perfectly acceptable definition of a Native American. Perhaps I should have said Indigenous Mexican. How about answering the original question?

The misused term of calling local indigenous people "Indians" dates back to the errant murderous Cristobol Colón. He thought he was in the Indian Ocean of Asia and was appalled that the locals dared to resist being raped, pillaged and enslaved. How many years must an error be perpetuated before someone thinks to correct it? Same with using the word "American" to refer only to someone from the United States. It's like reading incomprehension on a massive scale!

Native Americans inhabited America from Tierra del Fuego to the Northern Territories. In what is now the United States as well as throughout the Caribbean campaigns of genocide were carried out against them.

So which native people are you referring to? There are many and apparently all don't have exactly the same genetic origins.
People from Mexico show stunning amount of genetic diversity

But here we are once again getting distracted by unimportant minutiae.

I'm fully aware of the origin of the word Indian when used in reference to the indigenous population of this continent prior to Columbus' arrival. Whether you like it or not, it is in common use. For example: a local tribe here in Montana is called Nez Perce (French for pierced nose). They were so named by French Canadian trappers - in error - after a neighboring tribe who did, in fact, pierce their noses. These folks never did, but even today they even refer to themselves as Nez Perce.
My reference was to the post by Zihuateco: "Your Latinos friends are not Latinos. They are Mexican". My question, which I prefer as not being "unimportant minutiae" still stands, unanswered.