Guess what? in forward flight when you raise the lever the nose pitches up - you add pitch to all the blades and the one on the advancing side sees a larger increase in lift because it has the higher speed - the result, due to rotor flapping (not precession) is blades high at the front giving pitch nose up. When you lower the lever, the opposite happens. Lots of helicopters have mixing in the control runs to oppose this so that a nose down cyclic input is given as the lever is raised and vice versa.
The argument in the hover could well be due to downwash effects but a helicopter is a different animal in the hover than in forward flight and collective/cyclic cross couplings are different in aircraft types.