Yes it is currently true that the closest you can get is Green River Utah. But if you are coming from the east, it might be just as easy to get there from Grand Junction, CO, since I can almost guarantee that 1) Green River won't have car rental, and 2) If it does, it won't be open at that time of day. The drive would be about 1 hour longer from Grand Junction, but I guess it is up to you to make that decision. At one point in time, Amtrak did run to Moab. The California Zephyr took the branch track that goes down into Moab's uranium mines to serve the town. But this required backing up for thirty miles, and added overall about an hour and a half to the schedule, so it was dropped.
Are you sure about that? That is the first time I heard that story. The Cane Creek branch (the line from Brendel Junction toward Moab) is 30mph track, so any trip up and back would be at least three hours. The reverse move could not even hold 30mph.
The Cane Creek Branch does not actually get to Moab. It was built to serve the Potash mining operation west of the town. It gets close to town, but at the closest point, it is inaccessible (up in the cliffs and passing through a long tunnel). Where it is accessible to a highway, it is miles from town. There is no evidence of any passenger stations on the line. If serving Moab was a desire, a bus connection from Green River would have made more sense.
The line is now primarily used to remove uranium mine tailings for environmental cleanup.