I am not so sure. Perhaps the true fallacy is believing (without qualification) that money is a poor motivator.
Would you work harder, equally hard, or less hard if your employer reduced your pay? Would you more meticulous, equally meticulous, or less meticulous in your work if you were paid a bonus for achieving a higher quality target?
Of course money is not the only motivator, and it is certainly not a suitable motivator in all circumstances, but that does not mean that it is a poor motivator.