The people ignore the stats because they're rubbish
Not sure I like the tone of the article any more than I like all the 'findings' of the report - if you don't trust peoples opinions so, I can only assume you prefer genial dictators over democracy? The Casey report does give a small representation of people opinions, and rather than dismiss them there should be found ways to assuage them through both education and an improved justice system.
The crime stats are for *reported* crimes, and for many smaller crimes, such as vandalism or minor assault, there's no point reporting them as the police tend to do sod all, or - as what happened to a friend of mine - suggest the victim was to blame.
As for punishments, yes we're too soft. The argument for any punishment acting a pre-deterrent is a false one - criminals don't commit crimes in expectations of getting caught. The risk part of the risk vs reward equation is capture rates, not punishments.
That shouldn't stop punishment being used to deter recidivism or moving to greater crimes - in some cases corporal punishment should be brought back. A private switching followed by some counselling and follow-up help in terms of home-life and education would do a lot more than sticking a teenager into a youth detention centre to learn how to be a better criminal.
I do like the map of crimes though, it might upset estate agents, but tough titty - people should have all available information when purchasing a property. If I paid 6 figures for a property with a high crime rate I'd hardly be too chuffed.