I'm not suggesting that you don't do as they say but having to return a speed controlller to zero in order to stop a motor sound to me like cheaply engineered electronics. I would expect 2 methods of stopping rotation. A normal stop button which would reduce the motors speed in a controlled fashion from the 'process variable speed' set by the speed control knob down to zero and then turn the drive outputs off. The second button should be the emergency stop which should immediately turn the output to the motor off. Normal use should use the first button.
Any machine with electronic speed control that only has the single way of stopping is to my mind a fudge and likely to cause issues with either the drive unit as suggested already and or mains spikes and radiated noise into other electronic systems local to the machine.
When I design anything if I don't want the operator to do something I ensure that the electronics wont let them.
regards Martin