I live in México far from Cozumel and Cancún (Guadalajara), but I can tell you that this practice of not flushing the toilet paper and throwing it to the garbage can is unfortunately used in many hotels and restaurants all over the country. It really disgusts me and I think it's really something anti higienic.
The thing is, In my house, my family and friends houses, and all other houses I've visited, the norm is to flush the toilet paper. Even in the university where I teach some classes, there are signs in the bathrooms asking to flush te paper and not to put it in the garbage.
I don't know about the drain in Cancún and Cozumel, or the septic tanks. I don't think those reasons apply where I live, I have the theory that some people use lots of toilet paper per flush and those people are the ones that clog the drains, and beacuase an hotel must serve every kind of costumer, they must prevent that from happening by asking everyone not to flush the toilet paper. Anyway, In all the hotels and restaurants I've been, I always flush the toilet paper (The idea of having a garbage bin in the room with used toilet paper, is more disgusting than my will to follow that rule), I just don't abuse the ammount of toilet paper I use.