For Gulutzan's boss, the man who hired him, one coaching characteristic above all mattered during the transitional period.
"His steadiness at the wheel,'' says Treliving. "He never changed, the message never changed.
"There was a lot of turbulence outside the plane but that's when you trust in your pilot to land it safely.
"When we were going through those difficult times, the fact that the message didn't waver - at all - was very comforting and reassuring. Instead of grasping and deluding ourselves into believing 'Oh, something magical will happen.'
"No. Glen's message was always: 'This is going to come. We're not getting it yet. But we will.'
"And they did.
"It's like putting your hand on an element on the stove and being told: 'It's not on.' You're still hesitant, right? You still think you're going might get burned.
"Only by putting your hand on the element do you know you won't get burned."
The Jack Adams Trophy goes to the NHL's top coach of course. If Gulutzan had a ballot, who would be his choice?
"Tough question,'' is the hesitant response. "I'd vote for …. Torts (John Tortorella) or Bruce (Boudreau).
"I think Bruce has done a great job with Minnesota. That team plays faster. I know the West so I can appreciate what he's done.
"I look at where Columbus has come from, non-playoff team to a hundred-and-something points. And not because John and I are friends.
"So one of those two guys."
And Gulutzan, the man most responsible for the buy-in and return to relevancy here, where would he fit into any sort of hardware discussion?
"No,'' he says, with a soft shake of the head. "Sorry. Don't see it. What I do see is the good people around me that have helped get this turned around.
"I look at where Dave (Cameron) has taken the powerplay. I look at the penalty kill now, where Paulie (Jerrard) has taken that, to a place that has confidence and swagger and can get things done in the heat of a game, came from 74 per cent and is gonna end up at 81. And I look at Gelly, Siggy …
"And I most of all I look at our players. When things aren't going well, that's when a dressing room can splinter. Our character guys, our leaders, would not let that happen."
Gulutzan's persistence, along with that of his team, has the Flames firmly back in the playoff hunt.
"Critically,'' notes Treliving, "he never lost the players. He had the room at 5-10. From the inside, you could tell.
"We struggled but it wasn't because the players were trying to fight the message or him, or had stopped listening or believing. They just hadn't gotten it yet.
"They trusted him. And he's pushing them, remember. Leaning on them. Prodding and poking. Hard.
"I think what you're seeing right now is the trust that's been building all year. Glen's talked the whole time about building those relationships so that when you have to take a withdrawal, you can take it and it's not personal.
"He's taking some withdrawals now."