Lu,
A small device like you describe is impacted mostly by its dynamic characteristics, so it really isn't acting like a larger rotor. A propeller is also more affected by inertia and less by aero forces than a rotor. So sure, a bike wheel and propeller and even helicopter rotors have some characteristics of a gyroscope--and it may be easier to teach gyroscopic precession--but that does NOT mean that gyroscopic precession is the correct description for it. Thus in answer to your question, this teaching IS WRONG, but suffices in some circles to get certain partial ideas across.
Now please let this be! Just be content that this is the way lots of people have been and continue to be taught--not just you. But don't let yourself believe that it is real.
If anyone else would like to understand this and are willing to let go of the dogma that they may have first been taught, check the other threads (search under "phase lag" for many of them or start a new thread) and continue to ask questions. I'm sure there are some of us who wouldn't mind responding.