The case before the Supreme Court concerns Amtrak's qualifications to make judgements about the freight haulers' handling of Amtrak trains. It has nothing to do with adequate capital improvements.
Correct. It has nothing to do with funding, or even if Amtrak is being delayed by the freight railroads.
The case revolves around the part of the law that required the FRA to set specific and enforceable on-time standards for freight railroad handling of Amtrak. That much was fine. What caused the legal issue was that Amtrak was granted
veto power over the standards set by FRA. The FRA standards had to meet Amtrak approval. That effectively meant that Amtrak would set the standards, with the railroads subject to federal fines for violation of those standards (with the fines payable to Amtrak).
The problem is that Amtrak is legally considered to be a private corporation, at least according to the law establishing Amtrak, and as often claimed by Amtrak. Granting a private corporation the authority to set federally-enforced standards constitutes law-making, and the constitution limits law making power to the government. The government does not have the right to transfer that power to a private individual or corporation. Imagine if the DOT granted General Motors veto rights over automotive safety standards - standards then enforceable on Ford.
Amtrak's argument in this case is that they are not a private corporation: that they are a government entity and, as such, they are effectively part of DOT and thus have the right to set standards. The Supreme Court will make the final determination, which could hinge on whether they consider Amtrak public or private. However, if Amtrak wins and is thus considered a government entity, that could open up a lot of other areas such as open meetings, adherence to public procurement policies, and the such that Amtrak presently says do not apply to them since they are a private corporation. They claim to be both public and private, depending on which benefits them for a specific issue. A court ruling that they are a public entity could end the benefits Amtrak gets from claiming to be private.
This case is a fascinating mixed-bag for Amtrak. They could win by losing, or they could lose by winning.