I would tend to agree - neighborhoods that are visibly cared for are, generally, less attractive to people who wish to engage in illegal activities - neighborhoods in which residents care for their property and public places ar emore likely to have residents who are likely to call the police about suspicious activity.
For example, I live across the street from a nice little part (1 block wide, 3 blocks long) - and every time someone does something destructive in the park, the neighborhood residents are quick to react, by calling the anti-graffiti group when the playground equipment, picnic tables, or control boxes for the sprinkler system are tagged, calling the police when there is alcohol in the park (illegal under the local laws - especially in glass, which is specifically prohibited in all parks with playground equipment) or teens are loitering on the street by the park, etc. My neighbors were quite happy when I bought my house, because it had been vacant for a year (it had been overpriced - after it was vacant long enough, the price went down, just as I was looking) - and I am right on the end of the park that was away from the busier street, and therefore more likely to be used as a hangout. It was harder for my neighbors before I moved in to get the police to move people on when people were loitering by what is now my property, because the property owner wasn't complaining - now that I complain too, the number of times complaints are needed have dropped. I'm happy to say that no one has tagged the fire hydrant on my lot in over 2 years (knock on wood), after I had to call the graffiti squad 10 times in 3 months the first summer I lived here, and the tagging on the playground equipment (which is right across the street from my house) has fallen off too. About a month ago, the parks department planted 2 dozen trees in the park, all around it, and some idiot decided to run them over with a car or truck twice in 4 days (the same 6 trees both times, and the porta-potty 3 times in the same 4 days) - the community uproar included at least 20 people calling the police, and at least 10 calling our local council rep - following which the police upped the patrols, and it hasn't happened since - not even the porta-potty - because it must have become very obvious, very quickly, that we were watching.
Where I lived about 10 years ago, however, there was less community involvement (lots of short-term renters added to this, I think - less commitment) and much more tagging and petty (and not so petty) crime. Tagging was more likely to occur on private property (I've not seen that at all in my current home, just in the park), and was not removed nearly so quickly. There was more vandalism and littering (especially booze bottles in the street), and more reports of break-ins and stolen cars (there's only been two in my neighborhood in 3 years, and one was stolen from an idiot who left his SUV running on the street while he ran into his house for something he'd forgotten).
The condo I lived in between my house and the previous neighborhood was in the middle - but it was a condominium community, with security cameras on the areas mostly likely to have problems, like the community mailboxes and the pool... so things like that didn't happen in the common areas that the cameras could see.
I think that what I'm trying to say is that community involvement is the key here - if criminals know that the community cares, is paying attention, and will report infractions, they will go somewhere that they can get away with their activities more easily.