Well, that's not right. He is clearly NOT staying stationary in that frame. Since it is moving away from him, he is moving away from it. What his acceleration does is keep him from being dragged along with that frame, since without acceleration, he is stationary in that frame.@Nearlynothing
You said :
"His acceleration can be measured locally, with accelerometers, so this can be defined in absolute terms, with no reference to coordinates. Now in this frame he sees the station failing to remain stationary, he interprets his own acceleration as a means to remain stationary in that frame."
An interesting angle, i'll have to let that sink in for a while.
From HER frame of reference, the guy on the train is stationary and the train station is accelerating away from both of them.
Here's another way of looking at it:
Take a frame of reference and grid it as XY coordinates. In that frame, there is a pretty girl at 0,0.
At 10,0 there is a train station and a train.
Through some means that we don't care about, the train station, in our XY frame of reference, begins accelerating in the negative Y direction. The guy on the train doesn't want to lose sight of the pretty girl, so he has to accelerate to stay on the X axis while the train station moves away from him. From HIS frame of reference, he is moving relative to the train station but NOT moving relative to the girl, he is maintaining his position is her frame of reference.