Some people in Ajijic and other places in Mexico, offer to rent their own private vehicle, which most of the time is not insured or they do not have the right Car Rental Insurance.
If you happen to rent a vehicle from a private non registrated company, please verify that the insurance policy in the vehicle says "RENTA DIARIA" (daily rent). If the policy does not say RENTA DIARIA, in case of an accident the Insurance Company will not cover the damages and you will be responsible to pay all the damages from your own pocket, also the person who rented the car could be sued by the Insurance Company.
Do not let them fool you ! Protect your safety and your money.