Purely in the interests of this forum, I am willing to make a special expedition to Italy to find out, contributions in support of this selfless quest are welcome.
Seriously, I hadn't noticed, so I have just trundled through my photos of little Italian streets.
As far as I can tell, and can recall, the copper doesn't turn green but weathers to the kind of dull copper you'd expect from an old pipe. It's probably something about their weather. They also have a lot of very old lead guttering and downspouts that have oxidised to a greyish green. The copper, in time, will probably end up more or less the same.
And naturally, what would be old and scruffy here is quaint and antique over there.