CSXT does own that line. Amtrak is not without recourse though. Several years ago it instituted an action against CSXT and some other host railroads about delays. I never followed the matter, so I don’t know what became of it, but I believe the Capitol on-time performance has improved. At one point it was pretty dismal. One thing that had probably helped more recently is CSXT adopting “precision scheduled railroading. Fewer (but longer) trains.