We just got back from Turks and Caicos. (Provo, not Grand Turk)
There has been a lot of crime there, as in many places. But, it is not focused on tourists. It is usually a more domestic/internal problem.
We stayed close to our resort in a developed and safer area... Did walk back to our resort before the last faint glow of sunset turned into darkness. We felt safe enough!
Common sense and precautions!
NOTE: with the situation on the Island, in general, not just crime - we are not planning to return.
I think the advice to stay in more developed and controlled (safer, not out of the way areas) is the way to go. We used to venture out a bit further.... But, now we don't.
We would stick with Princess excursions, or a known reputable tour/excursion outfit.
You shouldn't need to worry!