Not everyone is used to having strangers smile at them, and they may not quite know what to do. The averted eyes are probably just that the person wasn't up for social interaction, not that they were snubbing you. They are polite enough to smile back, so accept that.
I speak from experience - in fact, this happened to me today. I happened to idly glance at someone who was NOT facing me, and she turned at that very moment, caught my eye and gave me a big smile. I was exhausted and hot and sticky and wanting a shower, a meal and a lot of sleep, and I did exactly what you described: I smiled back, but I looked away.