I was looking at NJEMS.rutgers.edu for an EMT exam in Jersey. One of the exam dates stated "private registration" under status, while other ones stated "accepting registrations."
I don't know, but I'll take a guess. Sometimes when a large class finishes an EMS program they hold a NREMT test for the entire class that isn't available to the public.
MMiz is right. It's an exam that's only open to people who took a certain course. Sometimes these are set up for large classes or classes for specific EMS companies.