The following very definative answer has been added at Tripadvisor here
Cozumel Rental Car Insurance 101/Lost Wages Info - Cozumel Forum - TripAdvisor
Copied & pasted from another board according to the intro to the post & I'm doing the same
"When renting a vehicle in Mexico please be aware of the following:
U.S. Insurance companies do not make direct payment for damages outside the country.
By Mexican law, if your rental vehicle is lost or damaged, you will be required to make full payment of all expenses involved, before you leave Cozumel. If you refuse the local insurance coverage, your costs will have to be paid out of pocket before you can leave Cozumel. The rentadora will supply you with the necessary reports for you to recover payment from your insurance company when you get home. The same applies to medical treatment. Some of the local policies include medical coverage but, be sure to find out the limits & which clinic accepts their direct payment, or you will still be required to pay out of pocket & recover from the local insurance company later. Coverage & Deductibles vary with each rentadora, so read your policy carefully to see if theft, as well as accident, is covered. For example, scooters typically are not covered for theft or damage. Also, be sure to take note of what voids your coverage (e.g. leaving a paved road, unable to show valid drivers license or drinking alcohol).
According to Federal Mexican Law all scooter and auto rental companies are obligated to carry 3rd party insurance (Official Norm NOM-124-SCFI -1998) on all vehicle rentals, but not all rental agents comply. Ask to see this policy before you rent a vehicle and verify what it will cover in case of an accident. A rental company that fails to supply this coverage would not meet the standards that show them to be reputable. Never accept a vehicle that you feel falls short of safety standards. CRIMINAL PENALTIES: While in a foreign country, an individual is subject to that countrys laws and regulations, which can differ significantly from those in the U.S. and may not afford the protections available to the individual under U.S. law. The trial process in Mexico is different from that in the U.S., and procedures may vary from state to state. Penalties for breaking the law can be more severe than in the United States for similar offenses.
***If any person is hurt or killed as a result of an accident, then you will be subject to a detailed legal process and you will surely need the services of a lawyer and your insurance company and may also require assistance from your country's consulate in Mexico. If it is subsequently deemed that you are to blame for the accident, you will be detained until the other party (parties) involved in the accident are satisfied with any compensation offered by you (or by your insurance company on your behalf) or until your bail hearing which would be @ 24-72 hours from the time of your arrest. You could then be released by paying a cash bond to the court, but you would be a fugitive if you leave Mexico under this status before your trial is done. At any time that you reach an agreement with the injured parties and they sign the paperwork (pardon) you will be released from police custody and all charges would be dropped. Standard policies do not cover this expense. You can ask your rentadora if there is an option to purchase additional insurance that would cover this expense. So far as I am aware, none of the rentadora policies include this coverage. Fines, Towing fees and court costs also are not covered expenses***
Check for damages to the rental vehicle before accepting it to avoid the possibility of being charged later for scrapes & scratches already on the vehicle. If your rental vehicle is stolen, but found later, you are entitled to recover your payment, minus damage to the vehicle & rental fees. If you are an American citizen, be sure to notify the U.S. Consular Agent office if you have paid for a lost vehicle, so we can help you to recover your payment if the vehicle is found after you leave. Mexican law limits the # of passengers in a vehicle. If you exceed the limit for your style of vehicle, you are subject to a fine. Cozumel also has a seat belt law. Each passenger should check to see that their seat belt is operating properly before accepting the vehicle. There is also a hefty fine for talking or texting on a cell phone while driving.
Many parked rental vehicles have been broken into on the east side of the island. Do not leave valuables in your car or unattended on the beach.
Scooters, operated by inexperienced drivers, tend to cause the most serious injuries.
If you are not experienced with driving a 2 wheel vehicle, it is safer to rent a car.
If you rent a scooter , WEAR YOUR HELMET.
Red (no stopping) & yellow curbs (short stopping only) designate tow away zones.
The vast majority of accidents are caused when tourists do not yield way at a corner a simple rule of thumb is this : if you are in town, driving on a Calle (i.e. a street running east or west - perpendicular to the ocean) , you DO NOT have right of way. You MUST yield at each corner to the vehicles traveling on the Avenidas (i.e. a street running north or south - parallel to the ocean) even if you do not see a stop sign. Locals in Cozumel tend to drive very fast, so wait until you are sure that you will be able to clear the intersection before proceeding.
Above All : Drive Safely & Have a Wonderful Holiday in Cozumel !
Anne R. Harris
U.S. Consular Agent in Cozumel"
But yes, I do look very young for my age, because I HAVE NEVER SMOKED.
