There are cases where the threat of "not getting back to the ship if something happens" is a legitimate concern. But I don't think it applies to Grand Cayman (and for any other smaller ports) Assuming it was a transportation problem (i.e. the bus breaks down) it would not be a big deal. There are not too many places you could be broke down where you would not be able to taxi back to the pier. Same applies with Cozumel and many of the other islands. Its going to places like Tulum where you are bussed 1 hour away where you could be in trouble.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013