Since it generally takes the NYSW an extra 24+ hours to get a train between Syracuse and NJ, its probably just easier for CSX to wait for the line to clear and run the trains their own way. NS can handle priority trains on their line as well through Pittsburgh in a pinch. Also, because of past operations problems, I really don't think that CSX and NYSW are on the best terms. Thats why CSX originally pulled the run-thru's off the line earlier in the decade. There were stories of trains sitting on the Tier's sidings for 3+ days at a time.
Lets face it, the NYSW is basically a dead railroad being held on life support by the parent companies... There is no good reason why they even exist as NS and CSX could run their entire week's traffic on the River and Lehigh Lines without anyone looking twice. They sold their souls during the Conrail buyout and are living like trust fund babies to the bigger railroads but the funds could be cut off at any time... and probably will be. They have no connection anymore to connect with any other railroads and can only handle local traffic over the Tier. I think the only reason they are still in business as of now is the fact that they are doing NS a favor by maintaining the Tier and serving the handful of customers online that NS didn't find profitable. I would not be surprised in the next few years if we see the continued absorption of NYSW into the CSX/NS conglomerate.
If you ever have a chance of seeing more trains on the Tier, it definitely won't be from the NYSW.
I think it may be possible that NJ Transit might not be the perfect, infallible organization that most people assume it is.