You can't install AC units on the outside of your building in Rome to maintain the architecture, which is the same as saying you can't have any at all.
Of course it's not in every single building. Where I grew up we had AC, but where my grandpa lived for example you couldn't. Just saying that the root comment isn't completely wrong, it happens.
You can run an AC inside the building, you just need to exhaust the heat out, which can be done through a window. Do an image search for "portable air conditioner window vent" and you'll see some examples.
I recently traveled to Rome and in both places we stayed there were AC units mounted below the windows. We also saw some split systems that had the condenser unit either in a foyer/lobby (hooked up to a vent) or on the roof.
