Does powering both phases (left/right rotation) of an AC motor hurt it?
Figure 1. The motor shows two windings and an overload switch.
Those aren't resistors. They are the forward and reverse motor windings.



simulate this circuit &ndash; Schematic created using CircuitLab
Figure 2. The resistor symbol is hollow, the inductor (winding) symbol is solid.
My guess is that they're using some sort of shaded-pole motor. Depending on the construction, with both windings energised the magnetic fields may cancel out eliminating the back EMF and resulting in a much higher than normal coil current.
I'd err on the side of caution. The switch or mechanical relay contact almost completely eliminates the likelihood of simultaneous coil energisation.