I’ve never heard that story. I’ve only heard the phrase was common as it had to do with local prevailing winds, and which direction the soot would blow. If you were on the wrong side of the tracks, you lived downwind.
I sort of live on the tracks. In my area, some of the wealthiest and poorest people in the city are within the same distance from my place.
I live on the bad side of the tracks, across from the worse side of the tracks. 
Seems like the local train line’s a popular suicide spot, too. At least once a month, late at night, I’ll hear the train’s whistle suddenly blaring (there’s no grade crossing for miles in either direction, so there’s no other reason for the train to sound its horn) shortly followed by the fire trucks quietly driving down this residential street with lights on but sirens off. I wonder how many of my neighbors are aware of this?
I live, quite literally, on the wrong side of the tracks. I live in a quite well-off suburb of Montreal and the commuter train tracks divide the very affluent western half of the town from the only moderately affluent eastern half.