We want to have consistent forces upon the pistol, shot, after shot, after shot. If the support hand slips along the side of the handle of a gun, the forces upon the handle are not consistent which lowers the probability of consistently returning the muzzle down to the same location.
Support hand slippage is a very common deficiency and when you are aware of it, it's easy to recognize this issue, even during real time shooting (without the assistance of slow motion film).
Many shooters with this issue will recognize their support hand does not feel right after shooting a few shots, and they will instinctively recover and pull their support hand back to their original position. This recovery may look like they're covering up their mistake; however, they subconsciously know what "feels right" and are simply making the necessary corrections.