Not smart. Brave but not smart.
Never try to chase someone on their home territory. They have allies, you don't. People know them, they don't know you. And any group will close ranks around one of their own against an outsider even if the outsider is in the right. It is just human nature.
I witnessed an American grabbing some 'Roma' youths on a train in Italy, who were trying to pickpocket him, and some eldery Italians who saw it in action also got into it and grabbed those little kids and started to wallop the living daylights out of them, yelling "Chiamo la politzia", that kind of thing...the American guy had to try to cool them down. As it was, the kids got hauled off to the carabinieri at the next station. I think a lot of Romans are also fed up with petty crimes like that.
I dunno. We've helped hapless foreigners here in Seattle. If Italians prefer their own thieves to tourists... I'm quite happy to leave the Italians to their thieves and go somewhere else.