It would be easy to generate a wave of phony outrage about this incident, and I'm not going to do that.
No, the poor dummy should not have touched the statue. Never touch anything older than the United States of America. Yes, he's going to have to pay a restoration fee. The Italians have no money to maintain and restore their rapidly aging and deteriorating treasures.
Let's have a bit of perspective, however. This is not as bad as World War II, which destroyed countless treasures. This is not as bad as merely carting the thing off (the English, for example, have taken possession of almost everyone's treasures and have no intention of returning them). This is not as bad as letting an old lady "fix" the thing. This is not as bad as renting a hammer and a chisel in order to break off a few loose pieces (Stonehenge, to name an example). And it's not as bad as deliberately attacking the statue with the intent of destroying it (vandalism, throwing paint on things, hitting them with hammers, etc.)
So, as bad as this seems, it's not that bad. Give the guy a break.