Mexico has a system in place where you can check to see if a vehicle is stolen, before you buy it. But there are tales of the ‘owner’ and the ‘theif’ being in cahoots, and not reporting the vehicle as stolen until after the sale.
My case was simple. I took it in to transfer the title and it went away on a wrecker. Before it got that far I was being followed by the state policeman on site. He insisted on following me to the bathroom, at which point I asked if I was suspected of something. He had no answer. My lawyer was recommended by a friend. I was being charged with being the thief, and he had to extricate me from that, first, and then clear my record. We got to be friends during that time. When I applied for citizenship my record was clean.