The language is not similar, it's just in the same tree. There is a common linguistic ancestor that they all share but that goes back THOUSANDS of years. Imagine a Spaniard claiming to be pure Roman because of the Latin influence on Spanish and just ignoring the rest of their history? Same thing except add a few thousand years! Additionally most archeologist in the field think that the Aztecs were a group of mercenaries that probably took their language from the tribe they married into or were hired into, took their religion and culture from and after 100 years or so left or were kicked out and then went on to form their own city-state and the rest is history. Point being, the language of the Aztecs is not necessarily the language of their own ancestors and even if it were, it's an ancestor that was not Aztec! It's like saying I am from Africa because all humans are from Africa. Or that all Americans are obviously from England because they speak English. It's silly. The Aztecs emerged from a dominant culture that they borrowed their language and religion from.

Edit: To sum it up: There is ZERO evidence of an Aztec 'homeland' in Arizona. Period. It takes blind faith to believe a story like this and it's insulting to the indigenous peoples whom we do have thousands and thousands of years of archeological evidence for having inhabited these areas in Northern Mexico and Arizona. They share common linguistic ancestors that spread throughout an incredible large geographic area but these people are not and never were Aztec. Stop the madness.