Almost all dive masters/instructors are treated as independent contractors. Some shops pay them cash or under the table and those are not able to get Social Security even if they want to. The other shops pay them formerly with checks or cash and require facturas (reciepts) from them. Those are legal and may contribute what is a small amount towards their own social security and other government taxes.
Then I would suggest that all of those DMs & Instructors insist on legal contract work. It'd be nice if we customers could confirm compliance before doing business, and one member did actually suggest a possible way to do so - but not a reasonable one. Cozumel has come a long ways since the WWII vets came back to their old airfield with tanks and portable compressors to hire fishing boats to take them diving, including too many cruise piers in my opinion, and there is no apparent reason why Cozumel cannot resolve with Cozumel issue.
DAN Mexico coverage is unfortunately not much, $5,000 USD for local coverage I think, but if the pros have SS Medical coverage - they seem well covered, as well as possible. You all should see to that as much as possible.
As far as boat safety, other than Operator error, I don't know of any accidents. Sure, I'd like to ensure that the boat is safe before boarding, just like I'd like to be sure before boarding a ferry, bus, van, taxi, plane, etc. but there's not much I can check. The one time I requested Oxygen for a diver was at Coz and it failed, but should I start requiring every boat to demonstrate that their O2 kits are onboard and actually work?

Why don't you all there take whatever actions that you can to improve safety in that area so as to protect the name of the island.
I am already boarding boats with as much gear as I can carry in one trip, including my own floatation vest I wear while the boat is moving and the DM is strapping my BC to a tank - yeah I'd wear it on your boat too, I'm checking every tank for CO levels
for good reason,* carrying all the safety devices on dives I can - far more than most, and I think I'll start checking my tanks for O2 too since I have seen divers on Nitrox who thought they were on air for a deeper dive. I'm doing all I can I think, and hope Cozumel will do their bit.
* Yeah, the big fill station has Analox inline CO monitors thanks in large part to Dave here, and I hope they run them correctly, but there are a lot of compressors on Coz. I'd test tanks even from the big place with the monitors, but dang sure am going to test the others too.
Thanks for the info...!
