RBid, I believe in your theory, and although I have never really put that much thought into it, it is just in my nature to look at people, smile, and say howdy, good morning, or some generic pleasantry. But yes, it immediately establishes that you are alert, oriented, and paying attention. Just exactly what criminals do not want in a potential victim.
I also agree that women live under a different set of guidelines, and need to be careful about being perceived as "sending signals". Face it, we men are pigs deep down inside, most of us keep a lid on it and behave as honorable gentlemen, but there are some who will vigorously pursue any attractive female, eye contact or not. I think the idea of brief eye contact and looking away tells us a woman is aware of someone in their space but not interested in a date.
Always try friendly first, the world would be a much better place if we all just lighten up and be nice. This does not mean you should be naive, unprepared, or overly trusting of strangers, just don't go through life like you're navigating behind enemy lines.
