I looked and couldn't find any contribution by Gagger to this thread. I also read through Scotty's comments and can find no basis for paraphrasing him as saying: "the only thing that determines direction of the ball is the direction the foot is travelling at point of contact".
The physics are reasonably simple, the difficult thing is to repeat it time after time. We could make a robot foot/leg that would kick the ball over the black dot 99 out of 100 times (negating wind and ball issues).
There are two things that determine the direction of the ball:
1. The direction that the part of the foot that is impacting the foot is facing. (call it 'the face')
2. The plane on which the foot is travelling in relation to the target or face (call it 'the plane')
The 'face' more or less controls the initial direction of the ball, while the differential angle between the face and plane control the swing or sideways movement of the ball through the air. So someone that is kicking with a big hook (eg Thurston) would kick the ball with the foot facing a fair way right of his target, but his plane line (angle of attack) is even further to the right.
I would also assume that kickers would tend to have more sideways movement if they don't get 'over' the ball. Getting over the ball would help them create a more downward (or more likely less upward) strike, and cause more backspin on the ball, thus less side spin. Barnes is a good example of getting over the ball at the moment.