This may be a Had To Be There situation.
I also don't like the idea of forging a return to the forum after a several month hiatus and disagreeing with you twice in one day ... maybe I should wait until tomorrow.
Oooooh what the heck!
If possible, I would not stop the play where I had to go to the Alternating Possession arrow.
I may allow them the easy rebound and possibly, 'accidentally' stop play before the put-back opportunity. But I wouldn't want to potentially change possesions because of my whistle.
Just my two bits. Obviously an official could do whatever they felt fit the situation. Perhaps the rebounding ball was going to hit the injured player in the head as he lay on the floor.