Here's the deal in the Yucatan . . . You can purchase a car in the Yucatan on a tourist visa, but NOT register it or get insurance I your name, though as someone has said, you can drive it with permission from the person who has registered it. You need their written permission to drive it, even though you own it. The vehicle must be registered to get insurance.
However, if you visit on a tourist visa, but own a home in Mexico held in a corporation that you are a director of, the corporation may purchase, register and insure the car, and as a director, you may legally use it.
If you visit on a tourist visa and own a home held in a bank fideicomiso, you may purchase and own a car, but not register it in your own name (ie. Back to paragraph one).
So, in a nutshell, you can buy a home in Mexico (using a fideicomiso), but NOT legally register or insure in your name a car you have purchased.
Get it?