I don't see where it definitively says that. I believe it says something like "within reasonable limits" and that's the key. Lower tire pressures can distort the tire thread (and sidewall) and potentially reduce traction just like over inflation will. It all depends on the tire construction and the intended design perimeters of the tire.
For example, a drag racing specific tire is "designed" to run at low pressures and maintain a constant footprint. Take that same tire with the same pressure and go around a corner with it and the tread footprint will go to hell as the tire is designed to maintain optimum traction in a straight line. Street tires (and road racing tires) must handle both acceleration, cornering and stopping. In reality, the optimum pressure would be different for each of these traits. Since only one pressure is possible its either the best compromise or the one that will maximize the most desired trait/feature needed at the time. For example, on the track or autocross course higher pressure is often used to maximize cornering but sometimes at the expense of acceleration.