I think Doc is limiting Green's minutes & opportunities so that we can sign him for cheaper in the off season. This wouldn't be the first time that Danny & Doc did this.
That said, I'm in full agreement with this thread. Its not so much that Green needs more playing time, its that he needs the ball more when he's in there. At some point Green needs to stand up for himself and say "stop going to that terrible shooter Glen Davis. Give me the ball and I can do better." Heck, even Green's fadeaway jumper with the shot clock expiring went in and looked smooth.
Get Green the Ball.