What they might mean is that you can burn out a motor if you don't give it enough voltage to turn.
When this happens, the motor start coil can stay activated because there is no rotational force to disconnect it. These coils are only meant to operate for a few seconds, so they can overheat and burn out if left like this for too long.
Also, the motor itself will not develop any back EMF and so it could also draw excessive current even at the reduced voltage.
In some countries this low voltage situation is called a "brown-out" because lights glow brown or dull red due to the lack of voltage.
Refrigerator motors are very likely to get damaged this way.