Correction about the car:
The car sitting down there isn't on the Metropolitan Transit Authority (MTA) roster. Also, the siding is no longer connected to the mainline. Plus there is an elevator next to it that was large enough for FDR's car to fit in. Even more interesting is that the siding isn't under GCT, but underneath the Waldorf Astoria hotel. This allowed FDR to get to the presidential suite in the Waldorf Astoria without the public seeing him in a wheelchair going from GCT to the hotel.
EDIT:
Here's some more info about the car. Judging by how it looks on several TV shows that it has appeared on, and the dialog in the shows, it is supposedly extremely heavy, like it was armored and intended to carry something, or someone very valuable.