I think kids with a secure attachment who are allowed freedoms at appropriate times (and when they start wanting them) will have pretty healthy instincts. My older dd has not really pushed her independence much at all, but last year she started walking home from school by herself about once a week (4th grade, the walk is pretty safe traffic-wise but is about 25 minutes). The walks home also involved a bit of giggly wandering around and candy purchasing with 2 or 3 other girlfriends; I didn't comment much on that as long as she was home in a reasonable period of time. She always was, so it remained a non-issue. (I wanted her to know I trusted her.)
The city and neighborhood we live in are generally low-crime and very safe, so I haven't made a big deal about strangers (although we've had some general talks), so I was caught off guard when during the last few weeks of school last year she came home all out of breath one day, saying that a creepy guy had followed her. She described him and his behavior, and also told me about her excellent evasive manoeuvers (crossing the street twice and noting that he did, too, and then running like crazy once she was around a corner to shake him from her trail, which worked). I took her seriously and we agreed that she would have parental companionship to come home from school for the rest of the year.
Well, by a couple of weeks later there had been a whole series of stalking episodes, always by the same guy, always 4th grade girls from our school. The parents got together and provided our girls' testimonies to the police, who figured out who the perpetrator was (a mentally handicapped young man who had recently been released from 24-hour supervision). He is now under full-time supervision again and all the girls are more wary than before, but generally it wasn't as scary as it sounds because everything worked the way it was supposed to in order to protect the kids. (We also have a new security guard at the school this year.)
Anyway, my point with this story is that my dd had very good instincts and acted appropriately, despite not having been subjected to fearmongering or nightly news reports about abductions, etc. She also seems to have a good idea of who can be trusted and who can't without my making that explicit. (We have talked about finding a mom or parents with kids if you are alone in a public place and feel threatened.) So at least in her case, I think her street smarts developing well without a lot of overt coaching.
What is more difficult is helping them deal with peers who want to lead them astray. Still working on that angle.
DD1 (Oct 99), DD2 (Sep 02), DD3 (Oct 09)