I think different people may have differing ideas of what "counter-steering" means. That said, the correct way to ride a bicycle down a curvy mountain road is

I think different people may have differing ideas of what "counter-steering" means. That said, the correct way to ride a bicycle down a curvy mountain road is for the rider to put his weight on his outside foot and inside hand (pushing forward against the drop) until exiting the turn (and, in fact, the bike will feel "unsettled" if this technique isn't used).