I think the former is demonstrably wrong and the latter is only true of teetering rotors.
Therefore using gyroscopes as a way to teach rotor behaviour simply ignores the reality of basic aerodynamics - why would you do that?
If you want to be a pilot, learn some aerodynamics - if you want to be a physicist, learn gyroscopes.
Some of the advanced texts quoted here show that in SOME rotors, it is possible to explain cross-coupling effects using gyroscope tendencies but those aren't for PPL, CPL or even possibly ATPL study.
Dumbing down training to make it 'easier' is a great way to cause more accidents through ignorance.