As gokeefe points out, railroads are still common carriers. Their obligations have been greatly reduced post-Staggers, but not eliminated. The whole grand bargain Amtrak represented was that the feds would release them from their obligations of passenger service in exchange for allowing them to run it on their tracks. Again, I don't doubt many didn't expect how resilient this service would be, but the bargain was nonetheless struck, and is still the law of the land.
Looking at a broader sense, I think the system we have currently works fairly well. Yes, it's true that Amtrak running across freight lines imposes opportunity costs on the railroad industry. However, you see that legislative power used as a way to maintain a minimum level of acceptable service and bring the freights to the negotiating table for things above that. If Amtrak did not have this power, it'd look like VIA: unable to maintain any consistency or timeliness in their service provided on host railroads.
At least our way, both parties need to come to the table and agree on the least bad option for both of them. The freights see this as an imposition, but I see it as a minimum standard. A "floor" for service, so to speak. We'd have no passenger service outside the NEC and a few corridors if every Amtrak service had to be built to Brightline/FEC standards of rail infrastructure so that passenger and freight traffic would never interfere. At the same time, you've got to get the freights at the table to do infrastructure improvements if you want to run more than one or two trains a day; there's not enough capacity on your average single line otherwise. To put it simply: Amtrak needs the leverage of being able to unilaterally run a minimal service in order to ever do more than that.
In this particular case, I doubt the freights were genuinely trying to give Amtrak the runaround and outright deny them, but it definitely seems like they were stalling the process in the hopes Amtrak would lose interest/the political winds would change. It seems to me that now they're in a pickle, because they can't back down and set the precedent that Amtrak doesn't have to study the impact of running passenger service, but they also know that there's a good chance the STB/courts will say exactly that and further embolden Amtrak. After all, there's no legal obligation I'm aware of for Amtrak to do those studies. It seemed to me to be more of a "keep the freights happy so they don't tie us up on lawsuits they may or may not win" measure. One that Amtrak might not find neccesary to do anymore if the courts say they don't need to.