I'm sure that Cayman is not unique in that requirement. Any dive business that provides both morning and afternoon dives are going to have that constraint, I would think.
I'm still not getting this over-arching idea that Cayman is overly restrictive or "big brother"....
I don't think so either, but the island had gotten a reputation of being restrictive of divers in the past, as indicated by that old Undercurrent article and I think that the reputation is still circulating around out there. The perceived unwillingness to recognize certified solo divers has added to that restrictive reputation; and as we've read in this thread some divers have been unwilling to give Cayman a try because of concerns about diving freedom.
The difficulty (sometimes) in renting tanks for shore diving has helped to bolster the perception, but as we've learned here, that is likely due to private property issues and that's fine, I don't really want to drag tanks all over the island; but folks used to the diving freedom of Bonaire might find that restrictive.
My opinion is that the uneven application of practices across different dive ops has contributed to the "secret handshake" theory. Also, the tendency of some dive staff to invoke mysterious scuba laws and cite non-existent regulations whenever it's convenient has helped to perpetrate the myth.
I love Cayman and I am not trying to run it down, and I have had great experiences with a number of dive ops. I do appreciate that the Cayman dive ops are dedicated to keeping their customers safe. Also that there are very many dive ops working in Cayman, and that the island is visited by large numbers of tourists, including casual divers - so I guess some ambiguity is to be expected - but it can be frustrating when you are just trying to find correct and consistent information.