Well here's my confusion, and I never tried getting an answer because I largely avoid these discussions until Stan's book comes out. However, this particular subject is fresh in my mind because I've been learning about Poolology and trying to understand a little better what happens to the cue ball at the pocket opening. That's why I asked if you understood it for CTE.
My concern is this: If you take an L square (ruler) and match it up to the cushion nose the point of the square will be the extension of the cushion lines to the exact corner you mentioned. This point is about an inch beyond the shelf for my table. If I am shooting a ball into the corner from a 45 degree angle, that means I am shooting straight down the center of the pocket, and over the point we just found. If I now move the ob to the side rail and pocket the ball, it is obvious that I cannot make the ball pass over the corner spot. In this case, the ball hits the side cushion about 1.5 inches away from the corner spot. There is no other way to pocket the ball.
If CTE puts the ob into center pocket where the extended point is every time, then there are many shots that cannot be made.
On the other hand, if CTE puts the ob into the center of the pocket opening depending on where the ob is on the table, then CTE sends the ob to different parts of the pocket depending where the ob starts out from.
It's just confusing to me, that's all, and it is also an interesting question for the Poolology method. In that method, I understand that some shots put the ball more in the center of the pocket than others, but there is enough slop in even tighter pockets to allow the balls to fall. My brief experience with Poolology so far makes me inclined to believe this is true.