No, our perception of the crime rate would change, however. If the news media reported less crime, the only way you would have of perceiving crime is if it happened to you or someone you know.
The problem is that the news media presents exciting stories because that's what people are willing to watch. "Man's House Is Burglarized While He's At Work" sounds a lot more exciting than "Man Went To Work; Nothing Happened to His House While He Was Gone." But that less exciting headline is about what usually happens to most people.
I think it's fine for news media to report crime, but maybe they ought to add balance to those stories by also showing overall crime statistics so people have a sense of what's usual versus what's unusual.