Other railroads own the tracks (capitalism - because they built or bought them).
Amtrak uses the tracks through the graces of the owners. Amtrak passenger trains have last priority.
Amtrak schedules and freight schedules are exactly the same as the trains of the 20's, 30's, 40's, 50's and 60's prior to Amtrak taking over all passenger operations. Their New York to/from Florida passenger service is exactly the same, to the minute, as the Seaboard Airline's Orange Blossom Special and Atlantic Coast Line's The Champion.
Those timetables were established to allow passenger trains prime use of the tracks with freight taking over odd hours when the mile long freight trains would most benefit from reduced crossing traffic allowing for faster freight movement. Speed limits for freight are higher during off hours than during daylight hours.
Amtrak, through inefficient central planning and bureaucratic bungling cannot follow the timetables as private passenger trains used to do and thus freight takes precedent as they cannot allow their schedules to be disrupted by the inept operations of a government boondoggle.
Passenger trains, including Amtrak, have always been given the best time schedules for their needs and freight only takes precedent when passenger cannot operate on a regular time schedule.
To blame Amtrak delays on freight traffic is on a par with Obama blaming Bush for everything Obama's ineptitude has caused.
Track time is scheduled in advance to allow for the efficient fleeting of traffic by the owning railroad. If Amtrak were to remain within its allotted time slot, it would operate on time. The problem is, Amtrak can't operate with anything approaching the sort of efficiency necessary to stay within its slot, so once its window closes, it has to run against the flow of traffic.