TIOPS isn't a reliable source, so to say that Murray is feuding with Sullivan based on that TIOPS report is stretching to say the least.
Sullivan has had personality conflicts with some players, but it hasn't resulted in any good players getting moved out. I don't think that's an actual criticism, people keep saying "what happens if he pushes out someone the Penguins can't afford to move?", which isn't a justification for that being a criticism right now. Once he pushes out someone that matters, then yeah, it's a problem. Now? He pushed away Cole, who was traded for Brassard (I didn't like moving Cole, but it's not the end of the world). He pushed away Sprong, who was traded for Pettersson (which is a move I would have made even had Sprong been playing well). Until he actually pushes away a good player, the criticism just isn't valid. It may become a problem, but it's not one right now.
Again, the things you can criticize Sullivan for are systematic problems that he's either not changing or the players aren't listening to him about. But playing one young player over another? Pushing out some depth players that he didn't like? Those aren't criticisms.