That's correct. They can have red activated when stationary and hooking a car, and (only) amber while moving.
I once again refer to MCL 257.698, (5)(f), which states in part:
However, a wrecker may be equipped with flashing, rotating, or oscillating red lights which shall be activated only when the wrecker is engaged in removing or assisting a vehicle at the scene of a traffic accident or disablement. The flashing, rotating, or oscillating amber lights shall not be activated except in those circumstances that the warning produced by the lights is required for public safety.