pk, your local DMV agent in NJ probably iswn't even a state worker, they hire out to "agencies" that are private companies. So don't expect them to know the law.
Check out the NJ DMV laws online, on the state web site. Then check out the USCG regs on the vessel documentation web site (which may also mean a detour to read the US Code).
Or just email both NJ and USCG and ask for it in writing, I think you will find the USCG is right on this and the local rent-a-clerk just doesn't know boats.
Keeping the writing (letter or email printout) on the boat with your title papers and registration makes a good backup, in case you meet an equally confused watercop who starts the same discussion. "Here it is, discuss it with the Commandant of the US Coast Guard" usually ends that question. (G)