Nail on the head there Crab.
The problem with the original assertion is twofold.
1. Mathematical v Physical
2. Theoretical v Practical
You can replace the v in the original equation with theta dot x r. However the physics demands you specify a particular r or v. So only valid for a given point on the rotor.
The equation of lift is for an aerofoil which is a thing of theory. It doesn't give the complete answer for a wing and is far off the mark for a rotor blade which needs to account for variation of both tangential velocity and induced velocity along the blade.
So correct algebra applied incorrectly to a physics equation that is unrelated to the actual physics of the problem under consideration. Apart from that I'm sure it's OK
Just noted the use of the term Centripetal with Cf in the quoted post ... I would have used centrifugal myself.