Heedm, this rate of roll situation (I am very reluctant to call it a phenomenon) is apparent in every helicopter I have flown and many more besides - witness some other posts on this thread. Each of these helicopters is designed differently with different control systems, different number of blades, different direction of rotation, different hinge offsets etc. etc. The only common factor is that they all exhibit a tendency to roll better/faster towards the advancing side which rather indicates it is a generic helicopter fact of life and not due to specific rigging. The sort of thing you are probably alluding to is Sikorsky's 'starboard lateral lead' , evident on the Wessex and Sea King where the output from the mixing unit is modified so that on application of collective, the starboard lateral jack is displaced slightly more than the port to help counter increased TR drift and roll as AUM and therefore hover power increase. On winching platforms such as these, more TR drift requires more left cyclic to maintain station producing more roll thus affecting the proximity of the winch wire to the fuselage (presuming the winch is on the right).
I know that test pilots carry out a stick plot for sideways flight as well as roll response to ensure sufficient control margins remain for safe flight which is why I asked Nick if he (as a mega test pilot God) could shed some light on what I and others have noticed.
Inherent sideslip (due to the TR thrust) in forward flight would tend to produce an opposite roll due to dihedral effect and flapback which works in opposition to the roll rate 'phenomenon' so I am still stuck for an answer.
This might be one of those sort of questions I have been asked by students where the final answer is " It just does, OK"