I do not believe American Nationals are allowed to own property in Mexico.
My husband has a former coworker who bought a home down there to retire in. I'm not saying it's WISE to own property down there, the government could snatch it away just like (snaps fingers) that on a whim or in the event of political unrest..........(not that property ownership is any more secure in the U.S. with the SCOTUS eminent domain decision).