I've rented cars overseas and gotten a similar letter in the mail. Usually when I've been caught by a speed camera in Germany (don't need to explain much more there).
Yes, it was a real ticket issued to you and the government passed it on to the rental car agency after tracing down the license plate. (Or, in your case, Avis passed your contact info to the government)
In every incident I've received a physical letter from the rental agency telling me that I got busted and I should expect a ticket to be forwarded on to me once they get it. I've never seen an actual ticket in my mailbox or a supplemental charge on my card (like others have said). Apparently Italy is more on the stick about this and goes right to direct collection.
My colleagues overseas have said to just rip it up, there's no way they can collect from you short of an Interpol warrant. It won't appear as a collection on your credit report. I've returned and rented from the exact same companies and nobody ever said a thing about the previous tickets.
tldr: Yes it was most likely real (especially because of the pre-warning from Avis).