TBH its not even about planes of reference, it's just someone not understanding torque in this case.
We will say "the direction causing forward motion of the bike is positive"…
Magnitude of Torque from left pedal is 0.175 * Fl = TL
Magnitude of Torque from right pedal is 0.175 * F2 = TR
Now, assuming we are looking only at forces due to gravity (mass of rider * 9.81), and with pedals horizontal, the two torques cancel as one is opposing the other:
TL (left pedal forward) + TR (Right pedal backward) = 0
so no crank movement.
Sat on the seat but not pedalling we have:
TL+TR = 0
Stood up and pedalling (the point he's confused about I think) we have:
TL (left pedal forwards) – TR (right pedal back) = +VE, i.e. we have weight on the left foot and we "unweight" the right foot without pulling, meaning our resultant torque is positive. In this case the best we can do by unweighting the pedal is achieve the torque provided by the weight of the rider on one pedal.
But we're not that simple, and we can pull up while pushing against the other arm, to the limit of our muscles – we now have the situation where TL is no longer limited by weight but by the force on the other arm, the harder you pull up on one arm the harder you can press down on the other without rotating around your crank yourself.