Yes, Aztecs are Native Americans. Any peoples living in the Americas before 1492 or descended from Native peoples and are living today are Native Americans. I'm only speculating, but your co-working may have a certain perception of what constitutes Native Americans based on media portrayal. Many people think of Plains peoples who used horses to raid American towns and forts and fight the Union army, like the Comanche or Apache, as the only kind of Native American since they are commonly portrayed in Old West films. There is, in fact, a wide range of Native peoples who all lived many different lifestyles before and after the arrival of Europeans. Many of them were agriculturalists who made no use of the horse since the horse had not lived in the Americas for several tens of thousand years before their reintroduction by European conquerors after 1492.