Its not that Carnival owns it, but it is a "Cruise Terminal" (probably run by the government) for use of all the cruise lines that stop there. In any case the locals can not get in to the shopping area. I have been outside the fenced area. I didn't feel unsafe (at least no more than I would if I were in Jamaica) No one hassled me. I was in a group of 6 people though, I am not sure I would do it on my own.
Dwayne is correct in that there are more local sellers outside the fence, lots of local arts and crafts thing if you are into that type of thing. There is a pirate museum too. If you apply the same amount of caution you do in any other port you should be ok.
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