This isn't true. Amtrak has priority by law over freight in the US as long as they are on time. They don't get priority once they area late. What happens is that Amtrak becomes late and then they lose their slot and become further late.
The result is that an on-time Amtrak train has to wait for a delayed freight train, because it is physically impossible to do anything else. This of course results in the Amtrak train now being late, through no fault of its own.
I'm going to give the tried and true answer everyone receives (at airports at least): it doesn't matter why your late. It's your responsibility. You should've left earlier and predicted the future.
Amtrak should've already built their own rails and should be serving much more of the country. I dont know anyone who can even consider Amtrak for travel.