We rented cars for the winter for 4 years, Hertz, Budget & National at Leon Airport. Also had friends & relatives do the same. I contacted all my credit card companies and found which had the better coverage in Mexico, turns out it was my CITI MC. I printed out a copy and took it with me. When renting I refused insurance. I had to sign two credit card vouchers, one for rental, and one for repairs if necessary.
I was able to cut my rental cost for monthly rental by 75% or more in a couple of cases.
You do need be aware of two things. 1st, be very meticulous when looking at the rental car before signing. Make sure every dent & or scratch is shown no matter how small. Also check the tires, including that spare exists. Try everything, including side view mirrors. They often get hit and may be glued with temporary glue. Do not rush this step no matter how long it takes and involve spouse/others.
2nd, what you are agreeing to with insurance is that you will be billed for any damage to your credit card and that your responsibility to get the charges removed. When you look at card coverage, have a conversation with the card company about what you will need if a problem as varies.
Given this, I never had a problem.