I have never seen that happen before. I have seen replays on St. A #1 where the ball hit the flag stick on the fly and ricocheted straight back all of the way into the water hazard, but never had the flag stick catch the ball and throw it back. One heck of a catch, lousy throw. Just curious, were you able to tell if the flag stick moved? I mean did the stick bend backwards before if threw the ball back or did it just kind of shake. Whenever I have had the fortune of hitting the stick on the fly, it just seems to kind of shake before sending the ball where ever.
Your are correct that some aspects of the flag sticks reactive role relative to the laws of physics are skewed. Most commonly known to me is how when a ball slowly rolling on the green after an approach shot, taps the flag stick and bounces back faster than it got there, or better yet, rolls right over the hole and through the stick. Now that is creepy, how does the ball do that?
I have another question maybe someone can answer. I know that the flag stick can be removed, but I have never tried to remove it while the ball is in flight or rolling towards the pin. I am always to preoccupied watching the ball approach the hole and get excited watching the dang thing roll toward the hole not thinking that hey, remove the stick. Then, of course, it hits the stick and bounces off. If I had the quickness and presence of mind, could I have just removed the stick?