A coal fired plant combined with an electric train and transmission losses is more efficient both energy and emissions-wise than the equivalent ICE engines to transport the same people.
Hard to say exactly, but it's not crazy. But I doubt the difference is that large.
Diesel engines for locomotives are likely 40% efficient before accounting for the motor-generator section. A modern a coal fired power plant might be 40-45% efficient. So probably the same based on raw thermal numbers.
I suspect economically the electrification is a win.
Also over the future it's possible to run the electrified trains on electric power from greener sources, like solar and wind. Where diesel would require a big upgrade.
The Tesla fans can probably give you the details -- although they're still a little wedded to cars. A coal plant can use filtering much more elaborate than anything a private vehicle can use, so reportedly a Prius (35 MPG) has about the same emissions as a Tesla fueled from an all-coal grid.
I don't disagree with your general point (although I'll quibble a bit about non-carbon emissions; even heavily scrubbed coal emits a lot of heavy metals that aren't present in gasoline).
But what Prius only gets 35 MPG? Did you mean 53MPG? My old Prius with batteries that are getting long in the tooth still gets 40-45 MPG.
