The Flower Gardens is absolutely in US territory, regardless of the port departed from. The Fling is absolutely US territory, regardless of where in the world it is, as long as she flies the US flag, and is under US port state control. US port state control means inspected by the Coast Guard and flying old glory. We can be in Cuban Waters and you would be still in a little part of the United States. Now, treaties are signed between states that allow foreign entities to board and inspect, and if they find contraband or paperwork out of order, seize, but that's beyond the scope of this conversation. Gulf of Mexico jurisdiction is marginally as follows. The US EEZ starts at a line in the west at about the mouth of the Rio Grande and proceeds to the 26 degrees north latitude line and then east. Somewhere around the mouth of the Mississippi, the line jumps north for about 25 miles, curls around to the east, then starts curling south following the Florida shoreline 200 miles out. The line bisects the Straights of Florida at about 79 degrees west and runs east between Cuba and Florida. Then is the 12 mile limit, which stands as the federal water line. Anything inside 12 miles is in the United States. Then is the State waters boundary. It is considered 9 miles for Texas, Alabama, and Florida, but in reality it is 3 leagues for some of those states, or 10.4 miles. Louisiana changed theirs, but I don't know if the change has taken effect.
LewisEvans is correct, the captain's right to search knows no boundaries. If he suspects a person is carrying something in a cavity that is detrimental to the safety and security of his vessel, than a cavity search is completely justified. HOWEVER. Anyone who would do that to a revenue passenger would never have another one. If someone tried to board and I suspected they had something with them that would be detrimental to the safety and security of my vessel, I would refuse them permission to board and bound them over to the proper authorities. The Masters rights on a vessel are absolute. He has to answer to his port state authorities, to recognized law enforcement for the territory he is in, and to his home office. Aside from that, his word is literally law on the vessel. Don't mistake Masters Authority for what is right and proper for a charter operation in Florida. This thread is about charter operations 10 miles offshore, not high seas law.
The Master does not have to submit to local authority, sort of. If a Florida State Trooper came to my boat and asked to search it, I could say no. Same for Monroe County Sheriff's department. I may only be searched by competent marine authority such as Coast Guard. I have given up that right in the case of the Florida Fish Cops to be allowed to operate in the Florida Keys National Marine Sanctuary. However, if I choose to mouth off to a FSP Officer and tell him he isn't welcome on my vessel, I'll have CGLE here in the blink of an eye. They can search, detain me, anything they want to whenever they want, without a warrant. If local LE showed up, I would ask them to wait until the CG showed up, just because I don't know how boat savvy the FSP guy is, I'd rather have a representative from the flag state there to help keep the boat out of trouble.
Reckdiver may say to anyone who will listen that he is only a taxi driver. Oh, how I hate that term, and the Coast Guard does too. Turns out, they think that the safety record of US flagged dive boats sucks, and that's the main reason they think so. I'm not putting words in Reckdivers mouth, I don't know if he thinks he is a taxi driver or not, but am responding directly to KWS post above. The Coast Guard has recently promulgated an advisory to dive operations regarding recreational dive vessels and how they conduct business. The era of the Taxi Driver and the complete disregard for what happens to the diver once they get off the boat is long over. The diver may be responsible for his or her actions underwater, but the Captain is now responsible to give proper briefings before boarding, before diving, and between dive sites. The "I'm just a taxi driver" defense is indefensible. Hehehe.
The presence or absence of a customer GPS onboard poses no threat to vessel or customer safety. The Master is within his rights to search the customers bags, but taking such action is not politically astute while offshore. Confiscation of such a device if found is sketchy unless it is declared beforehand to be a contraband item, because such a device would not normally be categorized as such. Destruction or abandonment of the device would be sketchier indeed since the device proved no threat to the safety or security of the vessel. I still think you'd have a hard time getting a CG LE to not giggle when you filed the report.