Some thoughts from a “quasi”-resident (we own property on Grand Cayman and spend about 5 months out of the year on island, but it seems to be increasing every year)….
No one owns the reefs. I'm sure the dive ops are speaking metaphorically or colloquially when they refer to the reef as “our” reef. (The one minor almost-exception is the man-made cement pot reef at the Marriott. But I have snorkeled there many times and they do not and really cannot control who snorkels there. They can and do, however, restrict you from using their beach chairs, as they should.). There are many government mandated marked paths to the shore between properties on SMB. There were some cases where the properties (condos and hotels) were blocking the pathways. The government has started to crack down on this, in support of the notion that the shore is open and accessible to everyone.
There are locations where you would need to walk across private property to access the reef (e.g., Macabuca/Turtle Reef) and you would be using private property if you used their ladders, rinse tanks, etc. But we snorkel at turtle reef with no problem, and my guess is that if you showed up to dive with your own tank, no one would even notice. That said, I rent my tanks from the dive op when I dive there, and I think that is appropriate as I use their water hose, rinse tank, benches, etc., as others here have mentioned.
The whole issue of paying the on site dive op for your tank seems to me to be a pretty minor issue (at least for folks like me who do not own their own tanks). I’m going to pay someone, so it might as well be the on site dive op – and we’re not talking big money. I have dived with many of the locals, and they all have rented their tanks from the on-site dive op – so it does not seem to be a big deal for them either.
For any other publicly accessible shore dive locations, you can either rent a tank from divers Supply (and they can tell you about places to dive) or get your own tank filled at Pure Air in Georgetown (which is where I get my pony filled for $3).
Another benefit of residence is that many of the dive ops that run boat dives offer resident rates (I have received them from Red Sail, Living the Dream, Neptunes, and Dive Tech). For example, with Red Sail it costs me CI 40 for a two tank boat dive, and CI 25 for the monthly lion fish hunt two tank dive. As I prefer boat diving, I think this is a great deal – just a few dollars more than renting tanks for shore diving, and I can max my dive time on the reef.
Regarding healthcare, one of the reasons we chose to buy on Grand Cayman was the quality of the healthcare system there. We unfortunately are not getting younger, and we find we need more and more healthcare services each year. I am on Medicare, but have a supplemental policy that covers me for health care outside the US (along with many other extended coverage benefits both in and outside the US, such as no deductibles and greater coverage for more services). My wife has used the health care system there and has received more effective treatment than she has received in the US (and we live near Boston, the medical center of the universe). We also have a dog, and the veterinary care there is great as well.
I wouldn't let the shore diving situation be the thing that determined whether to spend the rest of my natural life (and perhaps even some of my unnatural life) in the Cayman islands. So far we love it here, and more so every year.