Not really the case. VR generally is predicated on V2 and provides a suitable delta V such that, for the AFM rotation technique, VR will produce V2 - OEI - as the aircraft passes screen height. V2 may well be increased in some situations to take advantage of the improved climb gradient capability associated with an overspeed V2 takeoff.
Well, at least the 737 performance software from boeing tries to optimize every take off, to do that it usually does not use the lowest V2/Vr combination but rather slightly higher to much higher speeds. Over 95% of all take offs have an increased V2/Vr combo. Difference between Vr and V2 is usually only 2 to 3 kts anyway which is not enough even for the OEI case to just reach V2 at screen height, therefore the recommendet technique is to fly the actual speed of V2 to V2 + 20 and usually it is at the higher end of the airspeed band.
So in all practical application V2 and Vr are not fixed values, they can be changed considerably to provide best possible performance or highest possible thrust reduction.