Cruise ships are "registered" in other countries for tax and regulation reasons, but still may be "based" (have a home port) in the U.S.
Yes, I know some are based here, but being based here is not legally binding like registration would be. The point being made in the show I watched was that registration outside of the US keeps the cruise ship out of the US law realm. So, to use the fact that the cruise ship is based in the US as a reason to place Amy on the US missing person's list and not Natalee does not make sense to me. Both missing persons went missing outside of US domain.