Simsi - 6:52 pm on Feb 10, 2013 (gmt 0)
I think it does matter but I don't think it's nearly as simple as most people think and it's impact probably depends on the signals contained within the query.
Take three examples: "play space invaders", "distance to the moon" and "things to do in London". If you think about how long each of those might typically engage a user, they are very different. Combine the first and third with return visit stats, the second with follow-up actions on Google, the third with page views, etc, etc and maybe there are clear signals there.
So, going back to the OP, time on site and page visit stats may or may not provide additional info to Google and where they do, it may only be useful when combined with other signals.
The problem of the sites not providing the correct info rising to the top may be because the terms you chose to search on aren't condusive to user behaviour ranking signals, or maybe there is a temporary exploit available or it's simply that page views aren't influencing rankings on that query.
But whatever way, from what I see in my niche, I am inclined to believe user stats are in play for certaian queries myself.