Hi there. I worked as a concierge for a while in one of the hotels here and I faced this questions MANNNNY times....you shouldn't drink the water from the faucets - noone does - not even locals. But it is okay for bathing, brushing your teeth, etc... everywhere you go bottled or filtered water is used. A trick to be 100% sure your ice was made from filtered water is there will be a whole or indention in the ice!
But, it is more or less inevitable that someone will get sick - be it from the food, water, or ALCOHOL. You can visit your doctor and tell them you are going to Mexico. Usually, they will prescribe you an antibiotic, usually Cipro, which is a miracle drug down here. The second you feel sick you can take one and within the day you should feel better. (You can also find it here at the pharmacies without a prescription.)
Hope this helps!
L