From my understanding and someone editing Wikipedia, Amtrak has priority by law [1], thought the Amtrak page mentions a time window which the trains must hit to receive priority [2]
Some legal changes (including the Rail Safety Improvement Act of 2008) improved conditions, mostly by setting standard rules for allocating usage - but the language of the regulations is still very flexible. There are also some issues around the difficulty of one train passing another on single-tracked rail with limited sidings.
1. https://en.wikipedia.org/wiki/Trackage_rights 2. https://en.wikipedia.org/wiki/Amtrak#Trains_and_tracks