US-based response here:
If you decide to boat on US navigable waters, you consent, by default, to allow any legitimate law enforcement entity to stop, board, and inspect your vessel, at any time. It is not all that common to be pulled over and inspected, but it does happen (more, I think, for training purposes than anything.) It's just a condition you operate under.
I have been inspected by the CG once: I think they were looking for people running dive classes off recreational boats (which is illegal here; you have to be a licensed Captain to conduct business on a boat); they checked registration, required safety equipment, asked if anyone was a dive instructor, asked if anyone had been or was being charged to get on board, then wrote it up while I chatted to the driver about the SAFE boat. They handed me the inspection report, and cut us loose. Polite, respectful, and reasonably quick.
Not a big deal. Entire episode, from lighting me up to letting us go, was perhaps 10 minutes.