It's not true that it has to be the only light source. All of the light sources have to be the same type and on the same circuit, which is fairly common.
Many AC motors are synchronized to the frequency of the power line, by the same principal that turbines in the power grid are. So 60hz AC often means 30hz = 1800 rpm motor, and 59.8hz AC means 29.9hz motor. So if you have LEDs with a half bridge rectifier and your machinery is 180 degree rotationally symmetric, it will appear to not be moving, even if the line frequency fluctuates.
Many AC motors are synchronized to the frequency of the power line, by the same principal that turbines in the power grid are. So 60hz AC often means 30hz = 1800 rpm motor, and 59.8hz AC means 29.9hz motor. So if you have LEDs with a half bridge rectifier and your machinery is 180 degree rotationally symmetric, it will appear to not be moving, even if the line frequency fluctuates.