You all realize the murder (or murder and rape) aren't the only bad things that can happen, right?
I think dismissing these concerns by tossing out numbers on murder stats grossly misses the larger point. And I think generally the people who do that are men who are good, respectful people, and thus they simply can't imagine the reality, because it is so far removed from the way they think. And that's a good thing, but it can cause some unfair assumptions about the women who are nervous about engaging with strangers. It can make them look unreasonable or paranoid or snobby. But the reality is that not everyone is kind and decent and respectful, and she has no way of knowing which type you are.
http://yourdailydish.com/man-harasses-belly-dancer-facebook/ Here's a semi-related story about a woman on Facebook who was contacted by a man. He kept asking her if she found him attractive. She asked him not to call her again after her repeatedly did and she did not respond. Then he got crazy, insulting her and messaging her again and again and again. Read it. And all that came because she asked him not to call her again and didn't respond to Facebook messages from a stranger asking if she found him attractive.
You wonder why a woman might look away when you smile at her, especially in a semi-isolated area? She probably doesn't think you are going to rape and murder her, but she may well think--for good reason and based on many life experiences--that there is a not-insignificant chance that even the slightest engagement will lead to harassment. It happens. So much. And people who are good and decent and respectful people have a hard time accepting that, because they and the people with whom they surround themselves would never behavior that way, so it doesn't appear to be the reality of life. But it happens. Ask any woman who does online dating sites how many unsolicited dick pics she's gotten, or how many times she's been called nasty names for not responding exactly as the sender would have liked.
So yes, it makes women defensive. And no, that's not because we are too dumb at accurately assess risk. It's because experience has shown us that when we engage, it can and does turn brutal rather quickly, especially in isolation (like Facebook, or a hiking trail where there is no one to witness bad behavior). I'm sure it sucks a lot to smile at someone and have them avert their eyes. Having lived in Europe and smiled at people like an American is wont to do and a German is not, I get it. But try to understand that there's a good reason for it, shored up by plenty of ugly experiences.