I've never had a problem renting tanks for a shore night dive in Cozumel, just my buddy and I. I did a solo shore dive in Chaankanaab, again without any problems renting a tank for me alone. There was never any suggestion that I'd need a DM.
I have friends that dive off their own boat off Ambergris Caye - they certainly don't hire a DM when they go out. Off the Nekton Pilot at the atolls, all the divers do their own thing (only rule is no solo).
If there's any islands that would impose a DM, it would be the Caymans with their extensive regulations on recreational diving.
However, when I did my shore dives in Cozumel, I was on foot, or my car was stashed in a guarded parking lot at a beach filled with hundreds of people. In Grand Cayman, typical shore dives are in front of a dive shop (where you can leave your car) at Eden Rock, Turtle Farm, Cobalt Coast, etc.
In Bonaire, on the other hand, you might drive down a one-lane road to a beach off the road where it's possible you won't see another soul the entire time, especially in the off season. When J broke her ankle at Old Blue, we were the only ones at the site - it's very nice when you want the solitude, but also nice for thieves who can take their time rifling through your truck while you're at 80', and it really sucks when you have an emergency! (Fortunately, after about 15 minutes of figuring out I was going to get J up the hill and into the truck when she was already in agony, a couple other divers showed up and gave me a hand so we could lift her gently rather than drag her screaming).