The possession stats that you seem to live by right now certainly have their purpose, however, as everyone that uses them says, they still do not tell the entire story and you have to also use, to an extent, the eye test.
Just because a guy is on the ice for a lot of shots, does not mean they are quality, nor good possession, nor whether he is actually contributing to the thing that matters most...goals.
A guy can be on the ice for offense zone faceoff, which is won and they throw four shots toward the net with two wide, one blocked and one easily gloved by the goalie. They stay on for the faceoff which they win, it goes right to a dman who shoots it into the shins of the opponent, then trips over himself trying to recover and the other team goes down, takes one shot and scores.
Using corsi, that dman is a corsi positive 4 for that shift. Yet he fumbled the puck and allowed a goal.
Sure in the long run things will tend to even out, but that isnt always the case and can still be very misleading. If a player is often on the ice with other guys that shoot a lot and he himself throws a lot of worthless shots toward the net, but gives the puck away easily which allows for opposing goals would still provide a positive corsi number, but mean the player is also ineffective with a poor +/-, which I know is not a great stat, but when used along with this could be a good indicator. Green has good possession numbers, but is also on the ice for a lot more goals against than for. That makes me believe his possession numbers are just possession and not effective possessions, lots of shots toward the net, but arent going in the net.
I think that is what everyone sees with Green. While his numbers may lead you to think one thing, it doesnt mean its been positive offense, that is where the eye test comes into play. With so many flubs and goals given up directly, along with a rather lackluster offense (lots of shots missing the net and blocked shots), he just does not pass that test and I think the stats are rather misleading in his case.
And in the end, for me, its all about what I'm seeing, not about what all these stats, none of which are perfect, are saying.