Although driving in Mexico is on the right side of the road and the driving rules are much the same - the laws concerning road accidents and auto insurance are vastly different.
When driving to Mexico one should make sure their auto insurance is issued by one of the insurance companies authorized by Mexico.
Also if involved in an auto accident in Mexico, one is considered 'guilty until proved innocent' which means that if involved even in a 'not at fault' car crash in Mexico one is still very likely to spend some time in jail before cleared out by local legalities and procedures. Also driving without at least civil liability insurance in Mexico is considered a felony.
There are also some quirks regarding the specific of the Mexican auto insurance. For example vandalism is not covered under most auto insurances in Mexico. Almost always the car has to be physically gone in order to file a theft claim. Otherwise if you, say have a car window broken by someone, it is the owner who needs to pay, not the auto insurance policy.
And as a side note, almost all of the car leases in US prohibit driving a leased vehicle to Mexico.
