Believe it or not, I had an accident just a few months after buying this car. A motorcycle it me as I was making a right turn and he was trying to pass me on the right. I had no problem with the insurance paying, etc. The tarjeta and plates are in my name, so I believe the transfer was done legally. It's an older car, a 2009 Honda Fit, so I will likely keep it until it's junk. I paid the guy who helped me buy the car and he did all the work to transfer the title. It wasn't purchased from an individual but from a dealer in Guadalajara.
I think I'm good as for as protecting myself legally, but thanks for your help in explaining the process.