I'll be honest IP, I have no idea what those graphs mean, but I dispute every bit of it.
Usage is a statistic that calculates a guess on how many possessions a given player uses during a game. It accounts for pace and it is always done on a per 40 minute basis. Basically it says how much a player has the ball in his hands.

This is a graph with Usage on the bottom (x-axis) and FG% on the side (y-axis). It basically shows that aside from one outlier, which was 2005-2006 or Hedo's second year in Orlando, the fewer times Hedo touches the ball (ie, bringing the ball up, initiating the offense, dribbling, passing, etc...) the worse he shoots.
Here is the graph without the outlier:

This is a graph of the same thing, but without the 2005-2006 outlier

PER is a stat made up by John Hollinger which is an imperfect way of measuring a players' total effect on the game. Its basically a "how good all-around is this player?" stat. It has its problems but for this use, I think it is okay.
Here again it shows that as Hedo's usage goes down, so does his overall production. Basically without having the ball in his hands, hedo is half the player he could be (or was in Orlando..who knows what he could be anymore).
When Baron Davis, Antawn Jamison, and/or John Salmons are on the floor, Hedo Turkoglu won't get the touches to impact the game. When Hedo isn't a playmaker, he's not an impact player.
Even when he is a playmaker, he's still only a slightly above average player, but that's not the point. Unless Hedo only sees time with a backcourt of Fernandez/Matthews, he's going to be an invisible man, and a liability on defense against LeBron.