We have no idea what the hiring process of the Sabres coach was like. Obviously, both Murray and Pegula wanted Babcock. They backed up the money truck for him.
After that, we don't know what the process was like. Murray's input was there.
Given Murray's comments so far about the team, I find it hard to believe that the Sabres will fire Bylsma. Murray seems to be falling on his sword for failing to fix the defense. I believe what we will see at the 'end of the year wrap up', barring a major change or the team just falling apart, we'll see Bylsma and Murray both stay. Murray will attempt to fix the blueline. If Bylsma can't win with the team given to him next year, he's likely gone around the 30-40 game mark. And if that doesn't fix it, then Murray is probably gone too and we have a full front office reset.