What Agreements are Made between New Jersey Transit and Amtrak?

I am writing this in the form of a question and comment not as a complaint.  A minor situation today prompted me to ask about the relationship between two mass transit agencies.  I left work at about 12 noon today to meet a colleague in Manhattan to discuss a research project.  I arrived in time to catch the 12:27 NJ Transit train to NYC from Newark.  After the train stayed in the station for several minutes the conductor announced the train was being held in the station so Amtrak passengers from a disabled train could transfer to this NJ Transit train.

Since I had plenty of time, I was not annoyed at the 15 minute delay to allow Amtrak passengers board.  I question that if the situation was reversed and an NJ Transit train was badly delayed or disabled, would Amtrak allow NJ Transit passengers to board?  As reported before in this blog I do feel that NJ Transit passengers are treated like second class citizens of the rails.  It is very annoying when NJ Trains are consistently held back to allow Amtrak trains to proceed.  Hey guys, what’s the story?