Every group has its bad apples. Including your own groups. When someone in your own group (nationality, religious background, or skin color) did something terrible, I doubt any of you will ever relate that terrible person to yourself. Yes, you have nothing to do with him or her. You are two different individuals with your own thoughts. The bottom line is, you do not even know those people, and you are indeed unrelated and thus you are not responsible for what they did.
Somehow many people are quick to judge and categorize/generalize other groups. Anyone in those groups did something terrible, everyone (every single one of them... all of them) else in that group is automatically guilty by association. I'd be kind enough to call it (silly) when someone generalize people like that. You do not want to hear what I really want to say, if I use the most accurate words to describe people like you.
Anyway, it is not like the locals have 0 crime rate. It just will never make it to the headline like when some "Muslims" did this, did that.
On the other hand, I do agree that personal background should be checked more carefully when let in immigrants. When you just let in millions with minimal background check, you are letting in all kinds of people. The good, the decent, and the ugly...