Well, you can bring your own car, but it's risky and you need to make sure you really know what you're doing. First of all, you need to have insurance, and not Geico or AAA. You need to carry Mexican insurance. According to Mexpro, the policy you hold while you're in Mexico needs to be purchased from a company that is registered with the Mexican Department of Insurance, and that includes the following U.S. insurers: None of them.
If you do drive your own car in Mexico and you don't buy Mexican insurance, you'll be okay as long as you're not involved in an accident. If you are involved in an accident, though, and Mexican officials decide the accident is your fault, you will be taken into custody until you can prove your ability to pay for the damage. Yes, in Mexico you will go to jail for being uninsured, and kept there until you pay.
So really, if you're too cheap to buy an insurance policy during your visit, you should just leave your car at home. Sure, you probably won't get into an accident. But if you do, it's going to ruin your vacation. And probably your return home, too.
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