Yes, you were wrong. It's clear that you don't understand what 'across' means! :)
The word 'across' describes a movement crossing from one SIDE of something to the other SIDE. A train is very long and thin, so if you went across the train this would only be a distance of a couple of metres - say, from the window looking out on the left hand side of the track to the window looking out on the right hand side of the track.
If the man is walking the length of the train, from the front carriage to the back one, he is going down the train.
Think about the difference between travelling up or down a road (from one end to the other) and walking across a road (crossing from one side to the other) - it's exactly the same.