I really don't think it's confidence at all that makes Green play like he does at times.
He is just that kind of player mentally. A ton of it is just mental. He seems to think about spacing the floor a lot vs being in attack mode like some other players. And yes you will see the prettiest drives in the league from him and at times he looks like he just isn't willing to drive. That's his make up mentally, though I think he is growing past that some.
The mentality of players like KG, Kobe, Jordan, etc play with is a lot of what made them as good as they were. A lot of that shapes your game.