Nitrox appeared on the boat often (never requested it and didnt have to pay for it... many dives it helped stay deep on the reef).
Hmm. A number of my Cozumel dives exceed the MOD for 36% oxygen mixes even if you use a pO2 of 1.6, and I've had mixes that analyzed at nearly 38%. It's pretty hard to get mixes other than (nominal) 32% or 36%. If you think a max pO2 of 1.4 is more reasonable (as I do), then even with 32 your MOD is 111 feet - quite easy to exceed in Cozumel if you're not careful.
I'm not really sure what you mean by staying "deep on the reef." Perhaps you're referring to pushing the bottom of your planned depth for longer than you would with air due to slower nitrogen accumulation. Personally, I use air tables when I'm diving nitrox since my main goal is minimize my nitrogen load for a given bottom time, not maximize my bottom time for a given nitrogen load.
I'm also wondering if you travel with an analyzer since you don't request the nitrox or if the boat carried an analyzer that you used. I'm not an especially paranoid person, but if I can't analyze the gas I don't dive with it. On our last trip our boat left late and under some confusion due to a port closure earlier in the day. We discovered one less nitrox tank onboard than the total requested by divers. One guy had his initials on the teensy analysis sticker and said he'd personally analyzed it at the shop the night before. He ended up having to leave the boat at the SI due to another commitment, so we were back to enough nitrox tanks. The sticker he'd initialed said the contents were 32.3%. My analysis was 36.7% and the DM, who was curious if it was a mislabeling or an analyzer problem, got 36.5% with the boat's analyzer. I have no explanation for the discrepancy, but that's enough of a difference in MOD to prevent my ever diving on gas I haven't analyzed myself shortly before the dive.
Since I can't readily get my "best mix" for planned depth on a typical Cozumel first dive, I dive air. 36% is usually OK for a typical second dive.
Often someone would be sucking on DM's air.
Wow. All I can say is that that's my kid's air! In the incredibly unlikely event that my son's regulator fails at depth, he needs my air to make a safe ascent. If I'm not on that trip or sick in the room, he needs his buddy's air. If his buddy is so low he needs to nurse at the DM's backup reg, my kid is SOL. That DM now has 2 OOA divers and unless he's got doubles with 2 backups somebody's got to do a CESA.
Yes, I know this is unlikely and I know there are likely to be other divers in the area. In Cozumel, though, currents can vary widely at only slightly different depths and groups can quickly become separated enough that getting to a diver other than one's buddy when OOA isn't feasible.
In my opinion, once a diver is sharing air that dive is over for her and the pair needs to get to the surface as promptly as is safe, whether or not one of them is the DM or guide. Prolonging a diver's bottom time by sharing air with the DM is just asking for trouble.