Sutter's low fenwick/corsi/etc has a pretty obvious explanation (career, I'm talking...his possession numbers were trash with Cooke and Kennedy as well as just about everyone on Carolina)--weak players get knocked off the puck easily, don't win 50/50 pucks and aren't very good on the boards.
This is why Eric Staal can come to camp with a potbelly, sleepwalk through a season and still have decent possession numbers. If you're big and strong, reasonably coordinated and can cover good ground, your possession numbers will be positive, even if you're out of shape and don't give a crap. A smaller guy like Johnny Oduya just isn't going to be capable of winning any ice against him.
If, at some point since Sutter turned 18, he had spent a summer doing serious work in the gym and pursuing serious nutrition, I feel like about 70% of the flaws in his game would disappear and his possession numbers would go in the opposite direction. He's a 7 year pro now, so I'm not holding my breath for this to happen.
It's pretty confounding to me that he's never done this, by the way. His biggest weakness is obvious and the path to correcting it is well-trodden by just about all 1st round picks that make the show and aren't him.
I don't know if he ignores his strength trainers and coaches or if he has Crohn's disease or what, but I refuse to believe he's been told to put on 20 pounds of muscle over the summer any less than six times since being drafted.