Updated Gundam

OK, I think I understand now.

It is not gyroscopic inertia that is canceled in a coupled,
counter-rotating system, but gyroscopic precession. Gyroscopes, when an
attempt is made to rotate them in a direction 90 degrees to their plane of
rotation, react by precessing their axis in the third direction, 90 degrees
to both their plane of spin and the force being applied to their axes. The
direction of this precession depends on the direction of rotation of the
gyroscope. For example, attempting to rotate the axis of a
clockwise-spinning gryoscope to the right may cause the end you're pushing
on to dip; rotating a counter-clockwise-spinning gyroscope in the same
direction will cause the same end to rise.

A coupled system of counter-rotating gyroscopes cancels this precession
*for the system as a whole* -- but each individual gyroscope is still
exerting its precessional force on the point at which it is attached to the
coupling mechanism.

For a pair of Level-3 Oneill habitats, that's going to be a lot of torque ...

Steve