I know the USCG has agreements with the Bahamas. Haiti and the BVI as well as other islands that gives them authority as long as one enforcement officer from that country is aboard.
I did question the fact that we were flying a French flag and about 14 miles outside Haitian waters. OTOH, they had this BIG GUN on the foredeck of the cutter trained on us.

Basically Haiti claims a 200nm "Zone of Exclusive Economic Interest". That is primarily to protect fishing rights but it gives the USCG authority to board anybody regardless of nationality and the south side of Hispanola is (or was at the time) a popular drug route.