scubawife:I've done dives on the east side with Living Underwater and dives at Barracuda and San Juan with Liquid Blue. No matter how experienced you are or what certifications you have, Cozumel dive operators will usually not take you to the most advanced sites until they do a couple dives with you and asses your skills and air consumption. It's difficult to guarantee a dive to any of those sites unless you come with at least 4 divers who are all experienced. Otherwise it will depend on the skill and desire of the other divers on the boat.
Although some shops attract more experienced divers then others, I don't know of any who will turn away a less experienced diver. And even if you do get a good group it won't mean that everyone on the boat will want to dive a site like Barracuda.
You're hired! I couldn't have explained that better myself