I think people are reading too much into the Nemec stuff. Of course he's frustrated that he's not in the NHL right now. Any player in his position would be. I don't think that means the relationship between him and the organization has soured.
Unfortunately for him there's just no spot open right now. I think Kovacevic was probably looked at as being more of a depth guy when they brought him in, but then he and Siegs became one of the best shutdown pairings in the league. They have 3 set pairings that all work (although Dillon/Dougie can be an adventure sometimes) and they've all been healthy since Luke and Pesce came back.
They do have a tough decision to make this offseason though. I don't think moving Dougie is as easy or likely as people seem to be assuming it is, and Fitz is obsessed with tall defensemen so I think between Kovacevic and Nemec, he might choose Kovacevic. Which for the next couple years might be fine, but with Dougie only getting worse from here, you might end up needing another top 4 righty in a year or two anyway, which would presumably be Casey I guess.
On the other hand, Nemec has pretty good trade value, so if you are going to make a big move, he might be the piece for it.
It is nice to have this kind of "problem" though when you consider some of the bluelines we've iced in the last decade.