Just semantics, I guess. After re-reading Mark's post, I see his point about the the word "intentional" just describing the intent of the action, asa opposed to a type of foul. The only flagrant fouls that I've ever called have been technical fouls for fighting or dead ball contact, so I've never really considered a flagrant foul that would only be a personal foul. Since the penalty, 2 shots and the ball is the same as an intentional, the ejection is the only kicker.

Player Control, Intentional and Flagrant Fouls.
 

A personal foul is a player foul that involves illegal contact with an opponent while the ball is live. A common foul is a personal foul that is neither flagrant or intentional nor committed against a player in the act of shooting or tapping for a goal nor part of a double or multiple foul. A player control foul is a common foul committed by a player while he/she is on control of the ball or by an airborne shooter (NFHS & NCAA Women's).

Having said that, can a player in control of the ball commit an intentional or flagrant foul? The answer is yes.

Have I ever called an intentional foul on a player who is in control of the ball? Yes, I have had it happen just once in 30 years. A1 caught a pass from A2. B1 obtained a legal guarding position to the side of A1 just short of contact. A1 then decided to plant an elbow in the middle of B1's chest. A1 did not execute a normal pivot and make
illegal contact with B1. A1 could have easily dribbled away from B1, instead he looked straight into B1's face and then just popped him one in the chest. It wasn't enough for a flagrant foul but it was enough for an intentional foul. To compound A1's mistake, he committed the foul under B's basket so B got the ball under their own basket after the free throws.