P Factor Question

[rcav8r]

The accepted definition of Pfactor is that the prop disc of an a/c at high aoa produces asymmetric thrust between the advancing and retreating blades. This means on a prop rotating CW viewing from rear, the right half of the disc produces more thrust causing left yaw of the a/c. My question is, why isn't gyroscopic precession involved? As you know on rotorwing the cyclic input involves precession of the rotor discs, i.e. creating more lift on the right side of the rotor disc will cause a pitch up of the helo, assuming CCW rotorspin viewing from top. So, back to the CW rotating prop disc, why doesn't the asymmetrical thrust occur 90degs later causing a pitch up of the a/c?