the green play was a good no call. the contact didn't impact the shot, the play, or the game. although if Parker gave a harder contest on Ray Allen's game tying 3 and there was lower body contact, i'm not sure the Refs would have swallowed their whistles there...
The Manu drive was a foul, but you can't complain about not getting that call. Especially in those deciding seconds of games, if there is any doubt, they'll give it to the defense. Reason being, if replay shows it wasn't a foul, they don't want to gift teams undeserved points. Instead, they have to live with the possibility of the player making a shot anyway (like he would have if it was an and-1). That way, if they were right to swallow their whistles, they win, and if they were wrong to swallow the whistle, maybe the player can make a great shot anyway.
I agree with the "no foul" premise when up by 3. Why risk a free throw shootout. Its very possible to miss a free throw here and there, while you are gifting the other team a shot at free throws or an offensive rebound off the second free throw, making it a 3 or 4 point play. Instead, switch everything and force them to take a very low percentage, contested 3. This works a VERY high percentage of the time, and the few times it doesn't, fans and analysts go haywire saying "OMGZZ YOU SHOULD HAVE FOULED"
However, i very much agree with you that they should have fouled on the offensive rebound. Simple reason being, you know that on a rebound like that, you are in scramble mode, and usually (not in this case) on an offensive rebound there is an easy putback anyway, which would be those same 2 points. Or like we saw in our regular season loss to miami, when lebron almost lost the ball, our defense went into scramble mode, and he hit ray allen for what turned out to be a game winning 3. once bosh got the offense rebound, they should have hacked him. exchange free throws, then play tight perimeter D again