Aren’t you a Caymanian citizen? They definitely didn’t stamp my UK passport the last time I was there, nor my (American) wife’s. And that was for a flight rather than a cruise departure.
FYI, Ramira, in English the names of countries are (generally) not preceded by an article (the). The only exceptions that come to mind are Lebanon and Ukraine, and people seem to have stopped doing it for both anyway.
As the proponent of the assertion you have the burden of proof.
The problem is probably more widespread than we think. People that have already entered could have the virus. What about airport cleanliness ( bathrooms, railings elevators etc. ) I find it scary that with all that protective gear that bodily fluids an still contaminate !