It isn't the technique of playing a stop shot that opens up the pocket, as you might have already gathered, but to address it clearly, what was being talked about in the video is a drill for cue ball control. The slower you can make the stop shot, when you have to play a stop shot, the better your chances of making it. One thing that happens a lot in stun shots (which is what a stop shot is, head on) is the unintentional throwing of the shoulder from not stopping completely on your final back stroke. Another is the shoulder movement from the acceleration going into the stun shot. The slower you really need to play the shot, the better your accuracy will be, unless you have an issue with stroking slowly.
This can be put into a progressive drill, where you start with the two balls lined up to the pocket a diamond away from each other. See how slow you can stroke the stop shot, and when you get ten good hits, increase the distance to two diamonds, and so on. I think Tor discusses progressive drills in his videos. It is a great method for improving.
Well, yes and no. Making the pocket play bigger means one thing- you can hit the rail before the pocket and still make the ball. With a harder hit, you pretty much have to hit the actual pocket opening to make it. With a softer hit, you can hit the rail first, still make the ball, and the pocket can seem huge.
The rest of it is all technique. Technique meaning fundamentals. Such as shoulder drop that you mentioned. Improper techniques such as shoulder drop cause one to steer the cue to stay on line. On a harder hit, it becomes harder to steer the cue, and the loss of accuracy is much easier to see.
The reason a slow stop shot is so important to know how to use, is for position play. Most amateurs have no clue as to just how much one can hold the cb on an angle shot and keep it on the tangent line. So, they are looking at using rails for position when it isn't necessary at all.