Conrail did have a rail train. I'm certain, since I once saw it in North Central PA. That's not to say they had only one, it's also not to say that the one I saw still exists.
As to private owner rail train, might it be that CSX was simply moving a rail train from some welding plant to some place where the Gimpleton Air Line Railway (or whatever) was going to have rail installed by that private company?
I recall some years ago a Canadian National rail train showed up in the B&P yard in DuBois, PA. It turned out that B&P had purchased a few miles of rail from CN, who were taking up an abandoned line somewhere in Canada. CN had shipped it on their rail train (how else?) and allowed B&P to keep the train for a month or so while they dispensed the rail along their lines.
It was said that CN had instructed B&P "be sure it's empty when you send it back". Seeing some of the rail, I could understand why B&P might have been tempted to send it back.
Bob Netzlof a/k/a Sweet Old Bob