I think the decision to sit Bortz or Eddy has more to do with Dunn and Gunnar both playing injured than the debate of Eddy vs Bortz.
Dunn was obviously coming back from a serious injury and there was no telling how he was going to actually hold up to the physicality of the game. He could have easily taken 1 hit or another puck up high and then left the game early.
I also think that Gunnarsson is playing through a pretty significant injury as well. He was reported to have a lower body injury after the Dallas series and missed the first 3 games against San Jose. It wouldn't surprise me to hear that he actually came back before he was fully healed/ready due to the injury to Dunn.
Here are his game logs since he returned:
WCF Game 4 - 11:52
WCF Game 5 - 11:52
WCF Game 6 - 11:37
SCF Game 1 - 12:58
SCF Game 2 - 18:18 (OT)
SCF Game 3 - 12:44
SCF Game 4 - 16:28
In the previous series he averaged over 16 minutes in the 2 games against Winnipeg and over 15 in the Dallas series. I think he was injured in Game 4 of the Dallas series because he was closer to 18 minutes and then dropped to: 11, 13, 16 (2OT) in games 5-7.
If we sit Eddy and Dunn leaves the game early, Berube is stuck dividing Dunns minutes between Bouwmeester who is already playing 20-25 minutes, an injured Gunnarsson and then a mix of Petro/Parayko/Bortz playing on their offside. Over playing Gunnar could end up with him further injuring himself.
By sitting Bortz, we now have the option to split the minutes between 2 natural sided Defensemen in Gunnar and Eddy if Dunn goes down without over taxing an already laboring Gunnarsson. Between Petro and Parayko, who both play 25-30 minutes anyway, we still have the right side covered.