Your second sentence is correct, but it takes a lot more torque to turn a generator at a given speed when it is driving current through a load, than it does when it is open-circuit.
Inside the motor/generator, what happens is that if there's current flowing in the windings as a result of the EMF induced by turning the rotor, then, loosely speaking, it creates a magnetic field which opposes the rotation - but if it is not connected to some load (or a short-circuit) there's no current, even though there is still an induced EMF.
It's a standard case of the conservation of energy - if it were not the case, you could put an arbitrary number of generators on the same shaft, all supplying power to external loads, and then use the output of a couple of them to power a motor spinning the assembly...
If you are turning a motor/generator slowly, then the difference in torque is not much, but I am responding to the implication that the motor would have to be mechanically disengaged in order to disable the braking effect.