I think it's got to be a combination of both gyroscopic precession and out-tracking that turns a motorcycle. When you press on the handlebars, it makes the front wheel turn slightly. The gyroscopic precession, along with the front tire contact patch moving out from under the bike, causes the motorcycle to lean. As the motorcycle leans, the gyroscopic precession causes the front wheel to steer in the direction of the lean. That's what allows us to become a passenger after countersteering, while the motorcycle rails around the turn without any additional input into the handlebars until it's time to pick it up.
The gyroscopic effects of the wheels are why the manufacturers strive to make the frames so rigid torsionally. Flex in the frames was a principal contributor to the wobbles so common in older motorcycles when turning at high speed.
A better demonstration of the true effects of gyroscopic precession on the motorcycle is when motocrossers cross it up as they get big air. That is done by simply turning the handlebars. In that case there is nothing other than the inertia of the machine to resist leaning/rotating.
