Cozumel has a tourist based economy. It does Cozumel no good to make the tourists sick. All restaurants in Cozumel that are larger than a hole-in-the-wall belong to the restaurant association. As such, they MUST conform to strict regulations regarding sanitary conditions of their kitchens and careful food preparation. All water is purified. All ice is made with purified water.
Although some people do get sick while on vacation, it is impossible to truly know the source. Please do not drink 7 times the amount you usually do, eat food 7 times spicier than you usually do, lie in the sun 7 times longer than you would at home, and then blame the ice in Cozumel! Moderation is the key.
By the way, here at the minigolf we serve beer, homemade sangria, sodas by the can and bottled water. Everything is well chilled. We don't serve ice.
Hope that puts your mind at ease!
Minigolf Sally
Cozumel Putting Course