The confusion arises in terminology. What instrumentation engineers call a gyroscope is actually an integrating gyroscope or rate gyro, and what they call a gimbal in gimbal lock isn't the gimbal used to mount the gyroscope itself - the gimbals are used to keep a platform housing three gyroscopes level.
A standard gyroscope will point in the same direction at all times, while a rate gyroscope is used for measuring angular velocity:
The rate gyro will deflect the springs in proportion to how fast the frame is spinning - the faster the spin, the larger the springs deflect, which via strain gauge or similar measurements engineering, can be turned into an electrical signal. Measure the change in rate to derive the angular acceleration. Have a computer integrate the rate over time to derive current angular position.
Note the pivoting gimbals for this device though - they are in the exact configuration of a gimbal lock. A rate gyro's housing can only measure changes in a single axis. If the frame housing the gimbal moves away from the axis, then the device wouldn't measure properly. So, three rate gyroscopes are required to measure angular movement in all three angles. These are mounted on a platform that maintains a fixed orientation in space, so the rate gyroscopes can function properly.
When the rate gyroscope feeds a porportional signal to the instrumentation panel, it also feeds this signal to three motors. These motors are the torque motors in the quote. They turn the platform in response to the signal, keeping the platform level. When these gimbals keeping the platform level lock, then there is the problem, and the goal is trying to keep the feedback loop away from turning the gimbals until they lock.
The plan to turn the pitch gimbal 180 degrees would essentially turn the platform upside down, which would revese two of the three accelerometers - and all of the rate gyros. Specifically, the pitch gyro would now be spinning in opposite orientation after the platform was upside down (counterclockwise instead of clockwise). This would mean that it reads a 0.05 rpm counterclockwise turn as instead a 0.05 rpm clockwise turn - and the feedback loop to the motors would similarly be reversed, pulling the platform out of gimbal lock. This could be compared to jumping over the discontinuity at 90 degrees for the tangent function and continuing to perform the integration - in theory. In practice, the system never worked.