> I was under the illusion that Big-O was always asymptotic complexity (ie worst case) and that other notations (little-o, big-omega, big-thetha etc) were used for best/average/etc case. Perhaps I'm wrong, however.

No, asymptotic notation only refers to the behaviour of the function (or algorithm) as you take the limit N->inf, e.g. changes to the size of the input. But the nature of the input often changes the behavior as well.