if the rider leans out of the turn enough, then you don't counter steer, you just steer.
that is, if you can keep the bike vertical (on a flat road), then you'll never need to countersteer it.
This after all is the principal of the hack, which 'steers' and does not 'countersteer'. If you use your weight to provide the same reaction as the third wheel, then countersteering doesn't work.
This balancing, imo, is why you can change the steering of a bike at low speed betweeen 'steer' and 'countersteer'. At higher speeds (or lower ones with very tight turn radii), your weight and lever arm aren't enough to balance the bike, so it must always countersteer.
He immediately paid me the one of the highest compliments an Advrider can receive: "You're nuts!" (Alcan Rider)