Except it's not.
Doughty has played 300 even strength minutes. Around 50 of them have been with the 4th line. That's around 17-18% of his total ice time.
For comparison:
Muzzin: 264 ES minutes, around 45-50 with 4th line. Around 20% of his total ice time.
Ehrhoff: 183 ES minutes, around 40 minutes with the 4th line. Around 21%
Martinez: 253 ES minues, around 40-50 with 4th line. Around 19%
McNabb: 267 ES minutes, around 40-45 with 4th line. Around 16%
By percentage of total minutes, Doughty and McNabb play an amount similar to that of his teammates, and little less actually. Sutter does a good job keeping it balanced.
Also, when Doughty is out with the 4th line his corsi is at 49.4%. Hardly affecting his numbers by any considerable amount. That's respectable considering it's a 4th line of not very good players and he is nearly at 50% possession.
http://stats.hockeyanalysis.com/showplayer.php?pid=1001&withagainst=true&season=2015-16&sit=5v5