If you can't prove that there's a problem of any significance, it's not playing "dumb deaf and blind" to say that you have no prove of any problem of significance, it's stating fact.
That's exactly what happens in some places I've lived in, it's a small village, everyone knows everyone, almost no crime, people don't feel the need to lock their doors. You know what it's called when you make people scare of a problem that you can't prove exists? It's called fear mongering. It's usually done by people who hope to benefit from it.Do you lock your doors at home? If you have never been robbed, why do you? After all, no proof you are going to get robbed right?