Hi PT -- We discovered this first by accident, but then had it reinforced through working with Tom House (NPA founder and current USC Pitching Coach).
How you grip the baseball impacts how much force you can apply to the ball. Ex: Fingers together on a fastball grip, with thumb & middle finger splitting the ball in half, allows you to apply maximum force; Split finger grip reduces the amount of force you can apply to the ball.
The set (angle) of your hand and forearm are what impart rotation on the ball. Hand directly behind the baseball for a fastball; full "karate chop" for a curve ball; half a karate chop for a Slider; palm pronated away for a change-up.
My son has learned to set his grip and forearm angle in his glove (before starting his delivery), and to then just throw everything like a fastball (thinking fastball). He is not trying to twist his arm in mid-delivery, or snap something off at release. Logic and science tell us that this is also the safest on the arm.
When he wants the ball to fly perfectly straight, he grips across the 4 seams (thumb & middle finger cutting the ball in half), and sets his hand in his glove so that it is directly behind the baseball.
When he wants the ball to tail, he grips across the 2 seams, T & MF cutting the ball in half, and sets his hand in the glove directly behind the baseball, or ever so slightly pronated.
When he wants the ball to cut, he grips it with the 2 seams, and sets his hand in his glove a little open (the side of the hand just laying on the leather.
He throws from a 1/2 to 3/4 arm slot, which adds a little whipping action. The beauty of this for him is that he grips the ball, sets his hand and forearm angle "in the glove", and then just throws everything like a fastball. Grip and arm angle take care of the force and rotation.
Since really locking this in (summer '07) he has been incredibly consistent, efficient, and effective. His mechanics are extremely repeatable, since he is doing the same thing on every pitch; adding to the effectiveness, because there are no subtle "tells" for a batter to pick up.
Coach House and the NPA folks explain this far better than I. You might want to check out their Art & Science of Pitching book and DVD series (www/nationalpitching.net).