The low rate does not include liability insurance. Your visa or master card cover for collision damage, but only for your own rental car.... Not for damage to other people, car, animal, or structures.
With liability insurance added, your price would double. I would not buy only collision damage for your car, as you are just duplicating insurance. Actually, you will be VOIDING the collision damage insurance provided by your credit card, which many cases has no deductible.
If you buy insurance, make sure that it is liability insurance and cover damage both to your car and to any thing you struck. And count on it doubling your cost. Your own autoinsurance might cover you also, you'd have to contact them. My insurance, USAA, only cover you if you are like within 100 mile from the US border in Mexico. So Cozumel would not be in that territory.
We rented an old old VW from Isis. They did not run our credit card until about 3 months after we returned. A little unusual. No radio, no air, but it served us well - the old stick shift.