I wonder if there's some aerodynamic effect of the boxes being upturned which facilitates this sort of thing. Perhaps if a bit of wind gets caught under the box, it creates positive pressure inside the box with an effect similar to the skirt of a hovercraft?

I think the main phenomenon must be that they are very stable that way up, and have about the right area of "sail" on the side of the box, and weight / friction coefficient of plastic so that it manages to bumble along, rather than fly like a paper bag or do nothing like, um, a brick.

If weelie bins were a bit larger at the bottom than the top, and a little squatter, that would be even more disconcerting, to see them crossing the road!