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Well, I think I figured it out:

I'm pretty convinced now that Gazebo wrenches only apply a torque to one object (and don't apply and inverse torque to a connected body). I applied that manually and everything works as expected.

In the inverted reaction wheel pendulum video above, An equal but opposite torque is applied to the pendulum when a torque is applied on the wheel. Reason behind this: https://physics.stackexchange.com/questions/147932/is-torque-independent-of-choice-of-the-point-of-rotation