Full Blooded aztec??

Okay, so my boyfriend is ALWAYS bragging about how hes full blooded aztec and how his grandfather was full blooded aztec. Personally i think thats BULL. In order to be full blooded aztec ALL your relatives would have to be aztec right? And thats IMPOSSIBLE. Aztecs have been gone for hundreds of years. And any full blooded aztecs would have been long ago. Am i wrong in my thinking? Or does my boyfriend really have valid reason for thinking that he is a full blooded aztec and his grandfather was as well?