The quote that I go by is the one I got from the commander of the coast guard academy when I asked what their jurisdiction was....
"see all the blue of the ocean, that's ours!)
The uscg and customs absolutely does not need any warrant ( for better or worse) to board a vessel within the 12nm limit "contiguous zone" That's been law since congress passed it in 1799!
www.gc.noaa.gov/documents/CZ05_final.pdf
Link to NOAA PDF of maritime zones and maritime law