This is a confusing question. "Blurring" (blurred pictures) is a function typically of too low a shutter speed. Good to great high ISO performance - and the RX-1 is just about as good as it gets there - allows you to keep shutter speed high in low light conditions. I would also agree with other posts that the RX100 is not 'terrible' in low light, at least not relative to other compacts, indeed it is better than virtually any other compact camera, but not the in same league as the RX-1 or any other full frame sensor camera. This also effects video, as this depends on sensor noise and low light ability too.
I do not agree with your statement about the RX100 having poor low light performance. I have no problem in this area. This camera has replaced my camcorder for shooting in concerts and drama performances. Having manual control and clear zoom during video is very nice.