Don’t know all the physics but there is quite a difference between a 20 lb bicycle with a 200 lb rider and an 800 lb chopper with a 200 lb rider.
As I understand it, countersteer is when riding in a straight line on a flat surface and the front wheel is turned in the opposite direction from the desired direction change.
When that happens the mass of the riders tends to want to stay in the plane and direction it is going and the machines wheels move to to the right if that was the direction the rider turned them. Now gravity pulling down on the whole mess with the wheels now located to the right of the center of mass helps the lean increase and the machine rolls up on the side of the tires so to speak. The lean is such, that like a coin, the wheels roll in a circle (Mass wanting to keep on and wheel wanting to fall over) but not in the same track. ( look behind you on a surface that leaves a track. )
Now, get your self crowded to the curb by a redneck asshat in a pickup where yo can’t turn the wheel to the right because it is rubbing on the curb. Most times you will crash to towards the curb because you can’t or won’t LEAN towards the pickup. So down you go.
But… If you will lean away from the curb, the machine will track away for the curb. The tire is running more and more on it’s side which allows more and more turning. That contact patch that is referenced up thread is helping you. (But, try riding hands free one of those fat credit card monstrosities that they make on TV for putting in a show case with the really wide, fat, stupid rear wheels and a real skinny front wheel way out in front.)
Now, more about not wanting to change the direction of mass.
A dead skunks appears in the riding track from under the cage ahead of you. Instant bad karma that. With a flick of the bars, the heavy motorcycle’s wheels can be moved as much as 8-12 inches to the side without hardly any turning happening for a short distance. So, with this flick movement, the wheels pass to the side of the skunk and your chest and head pass right over the top of it. The flick of the bars the other way, brings the wheels back under the center of mass and very little actual turning was done. A lot less than the distance the wheels were moved to the side.
The reason the locked steering will not work on a bicycle and will on a unicycle is that when the lean is done, the wheels are trying to turn in two different over lapping circles and not just one. It has to fall over.
Just as balancing as you ride along, there are constant minor movements of weight shifting and steering head movement.
Ride real slow and counter steering will dump you but actual turning or the front wheel in the desired direction works just fine. The human can not take out subtle weight adjustments. The things going on when the speed is so slow that “object in motion wants to keep on keeping on” is over powered by gravity reaction speeds and distance from the contact patch by the mass that a flat statement that all steering is initiated by count steering is not quite the whole story. When riding a bicycle or a big heavy motorcycle hands free I have not seen the machine or the resultant track show that the front wheel first turned the wrong way in a counter steer. On a long chopper with bad geometry and a wheel that is easy to see that has excessive trail, well, it don’t do that when riding hands free.
So tot he OP, no the wheel does not need to turn. To remain upright in a controlled condition for any distance requires some wheel turning. If a machine is welded up with the wheels perfectly in line, and you got a shove along in a perfect straight line and then leaned, the machine would start to turn as it crashed. So a turn was done. There was no condition stated that it had to be successful.
YMMV