Anise, this is one plausible way it could work for your story. The private railroad would have sold the historic station building off to the highest bidder. The station would then pass through multiple owners, each with a different plan for what to do with the station. Then the city would get passenger rail service to its "historic station" reinstated after a political campaign of some sort, with the private owner of the station agreeing to let Amtrak use the station (perhaps for a nominal fee).
This has happened before, as noted with the Oklahoma City situation.
In cases where passenger service has been operated continuously without a break, the station building is unlikely to both be in private hands and be in use as a train station. Usually either the original freight railroad still owns it, or Amtrak bought it, or one of the local governments bought it, or most commonly Amtrak abandoned the building and just uses the platform. However, when there's been a break in passenger service, it's actually fairly common for the station buildings to be privately owned even though they're used by Amtrak.
There are a lot more cases where passenger service was operated continuously, where the historic station building is standing right next to the platforms, privately owned but not used for train service, while Amtrak uses a prefabricated shack off to one side or just uses the platform with no station.
A really impressive situation is in Grand Junction, Colorado, which has one historic brick station (privately owned) in use as an office building, a second historic brick station (privately owned) is sitting derelict, and a wood-and-cinder-block building -- which is *also* privately owned, originally being a restaurant -- is being used as the current station.
http://trainweb.org/...il/grandjct.htm
http://www.greatamer...JT/Station_view