In Mexico, when involved in any type of infraction, you are guilty until proven innocent. And you are the foreigner. Keep that in the front of your mind.
Insurance doesn't come into play until it is needed. People suggesting using their home grown insurance or credit card insurance because "they never had a problem" are very lucky. They never had a problem.
Now let's say you do have a problem. You will be held by policiia until fault is determined. Remember the top statement?
Now, you will be held until you pay up for any damages you need to pay. Getting reimbursed by your home grown policy or CC after you get back home will not be your primary objective at this point. Getting back home will be. How many million pesos do you intend to drive around with in your bulging pockets?
Your home policy isn't worth the paper it's printed on while in Mexico.
Take the Mexican insurance. Too expensive? Then don't rent.
Your assertions are somewhat incorrect. If you are in a minor car accident in a rental car there will be liability insurance on your rental car as that is Mexican Law. All vehicles are required to have liability insurance. Many Mexicans do not have the required liability insurance and they will not wait for the Police to arrive.
Mexican Law requires the Police to do certain procedures regarding more serious violations, kind of like here in the USA. If you kill or harm some one with a car in the USA you will most likely end up at the police station. If you drive impaired and get caught you may end up at the police station.
You will not end up at the police station for a minor auto accident unless some one is injured or you are intoxicated while renting a car from a major rental agency.
Your auto insurance on your vehicles will not cover anything in Mexico once you drive a certain distance from the border. So comparing a private car to a rental car is inappropriate regarding rental cars in Mexico as the rental car is owned by a rental agency and is required to have liability insurance to be on the road.
Amex does pay the rental car agency for damages that are found to be your liability. When you return the car the agency does not ask you to give them a certain amount of money for damages, they charge the card eventually as they pay to fix the car. They also charge time loss of use for the car.
Bill