Actually, Italy has a relatively low crime rate, compared with the rest of Europe.
https://en.m.wikipedia.org/wiki/Crime_in_Italy. I think it's safe if the kids just know about the risks and protect themselves. The stereotype of Americans is that they're naive and trusting, and therefore easily tricked. For example, Rome has long been notorious for pickpockets, but you just have to be aware of that and you can protect yourself ie not keep your wallet in your back pocket, or wear your backpack in busy places, etc, there's lots of advice on the web.
I think knowledge is power and it's important for kids to be street smart about visiting Europe, that in some places, especially Rome, they are definitely going to be seen by some people as a target. I don't think you need to become paranoid or racist, but to realize that there are more people there who are predatory and dangerous than we are used to in North America. And it does seem that thousands of kids spend time there without coming to harm.