I suppose I come from a small town, because I never really thought that simply saying "good morning" made you a target of evil-doers.
Of course, you don't have to respond to people you suspect are actually planning to make your morning a little less good. (I must admit, when I confronted a burglar, whose first comment was ".... And how are YOU today?" I didn't actually explain to him that, all things considered, I'd been better.) But even in Bigtown where I live now, brushing off a "good morning" seems to be ignoring a minimal courtesy.
(Listening to music, etc., clearly comes under the "otherwise occupied" exemption. I would not expect people to remove earphones to greet strangers. But a smile or nod, say, if someone sat down beside them on the subway seems a minimal greeting that says, "Hello, I recognize you as a fellow human being, rather than ignoring you as if you were not there".)
I guess I look pretty non-threatening, because even in big US cities, I've not found many people who wouldn't say "good morning" back, if I said it to them.
It's not about being chatty. It's simply about returning a greeting, and proceeding on your way.