Not sure you are right about that - you need a point for a force to work around or opposing forces to create a couple - a pivot point essentially, and that is the C of G.
No, you do not. There is no pivot with a helicopter in the hover. A couple is a couple is a couple.
Force x arm = moment
And every couple has its moment, it does not have a pivot.
This is a matter of static equilibrium and pretty straightforward. If things begin to move then it starts to get complicated and inertia brings the CoG into consideration. Then:
P of F is just a simple explanation of things we know happen, it isn't scientific or mathematical proof.