No, the criticism isn't because people get caught up about CO2 -- it's because "cleaner than other coal" is a very low bar to meet to be calling something "clean" full stop.
Also "clean coal" is not a type of coal being burnt (although that does matter too) but pollution control systems added to coal plants.
The doesn't cause acid rain version is called "clean" and that seems pretty fair to me when the other version causes acid rain.
Anthracite burns clean enough to use in a pizza oven. If your neighbor told you he was going to install a new furnace and offered you the choice of it burning wood pellets or anthracite, from a smell standpoint you should absolutely choose the anthracite.
Anthracite, in these regards, is very different from bituminous coal.