When I read the OP's question, the first thing I thought of was liveaboards in the Bahamas, too. We also did the Cay Sal Bank trip on the Nekton and that big boat looked like a square building sitting on the surface when you came up, there was nothing else around; but I was also thinking about the Exumas on a different boat.
One time in the Bahamas the US Coast Guard stopped our LOB and searched our cabins (for drugs I guess?) but they didn't find anything and left - I think that we were near Bimini. They didn't have warrants and we weren't in US waters but they had guns and so they did it anyway. The Captain just shrugged and said "it happens".
Another time, this was in the Exumas, we were moored near the wall and a US naval boat that turned out to be a sub tender was hanging around when a submarine suddenly erupted out of the water near near us - that was a surprise!
We also once got buzzed by US navy jets while on a LOB in the Bahamas.
I am sure that Cuba was the reason for all the attention given to LOBs in the Bahamas, and probably smuggling, also. I wonder if it is still the same, we haven't done a trip to the Bahamas in awhile.