Only been to Coz twice. I was pretty sick a few days after getting home but it was a cough from the air in the plane and fellow tourists. Never been sick from food, eaten tacos off the street. BTW, AVOID Skyservice from Toronto to Cozumel! Late several hours both in and out which added to stress.
Cozumel is really clean compared to some places in the South, it is hard to imagine there is any particular bacterial problem there. If you go to San Andres Island, you will find much worse food hygiene. And much worse, someone got Ciguatera in SAI from the fish buffet, his hands became bloated like gloves. Don't even ask, it ain't going to happen in a place like Coz. But obviously, cold food on buffets are asking for trouble. If you want to avoid getting sick, forget about all inclusive hotels, that is IMHO.
For those who got sick easily due to a naturally frail gringo constitution, you must get on an antibiotic before getting on the airplane, and end them after getting back home.
I think the one of choice is
http://www.levofloxacin.com and after getting sick in Bogota, Colombia after coming home, three little (but expensive) pills and it was all gone. I got that from my expert travel doctor, Dr. Jay Keystone, who was at Toronto General Hospital, but now is at Medisys Travel Clinic in Toronto. He was in Machu Picchu last year, so he knows his stuff.
Copious amounts of tequila will do it apparently as well. Get a bug from the top of a can of Tecate? Hell, I use Tecate to disinfect my toothbrush. Sure, if you drink tap water, you deserve getting sick.