However, if you make a toy gyroscope with the ability to flap when torqued, it would behave just as the regular toy you're familiar with. I suggest that it's the exploitation of the power of the airflow around a rotor that makes the difference, not some sort of cancellation of the couples and angular momenta involved because there's a hinge.
Perhaps you should write to the world's helicopter manufacturers and advise them they've all got it wrong.
I'm not prepared to try to advise you any further because you obviously aren't prepared to listen and believe you know better than any professional, in any case.
This is a case of Lu Zuckerman all over again. So many incorrect perceptions of basic principles.
So I'm out. I've got helicopters to fly.