And the Cowboys surely don't need Murray to be Julius Jones (unfilled potential).
What the Cowboys need Murray to be is the guy who plays with a chip on his shoulder.
They need Murray to remember that five running backs were taken before him in the NFL draft. They need Murray to become a consistent 1,000-yard rusher and someone whom coach Jason Garrett can depend on for 18 to 20 carries a game.
"I was definitely overlooked by a lot of teams," Murray said. "You have a chip on your shoulder. You get five other players taken before you. I had a great career at Oklahoma and I don't take anything away from those organizations. They saw what they liked in those other players. I'm glad I'm where I am at."
It's easy to make the excuse that NFL running backs don't get 20 plus carries anymore. It's easy to say running backs get banged up and their careers fizzle after four or five years.
You have to move on from that and play the best players for as long as you can -- especially if they're producing.
Murray didn't get his chance until Felix Jones went down with an injury. Jones, who had taken over as the starter when the Cowboys released Barber, rushed for 241 yards in four starts before getting hurt against New England and finishing with just 12 yards on seven carries.
Tashard Choice got the start for the Cowboys the next week, but it was Murray who burst onto the scene with a franchise-record 253 yards on 25 carries.
Murray went on a tear the next six weeks.
He became the first Cowboys running back since Julius Jones in 2004 to have consecutive 100-yard rushing games in a season. Over a three week stretch, he rushed for 466 yards, tying for the fifth-most yards all time by an NFL rookie over that span.
But Murray's season ended prematurely when he suffered a fractured ankle against the New York Giants in Week 14. He finished with 897 rushing yards and two touchdowns in 13 games (seven starts).
"You never want to take anything for granted," Murray said. "That's how I live my life on and off the field. I try to work hard no matter what, no matter if I'm doing well or I'm doing bad."
Murray has made plays throughout the entire offseason and in training camp. He has shown speed, lateral movement and power. He's not afraid of contact, especially inside where some questioned whether he would be able to take the pounding.
Murray is also showcasing his versatility. He's catching more passes out of the backfield and beat Sean Lee for a catch the other day in camp.
And when you talk about the core group of players for the Cowboys, Murray's name needs to be mentioned.
But there's one big caveat.
Murray has to avoid a sophomore slump. He has to build off his rookie campaign and have a 1,000-plus yard rushing season to prove 2011 wasn't a fluke.
He's got the demeanor and talent to withstand the pressures of the job.
Nobody knows if he'll be another Emmitt Smith, but it's clear the Cowboys have yet to find a competent replacement for the NFL's all-time leading rusher.
And at some point the Cowboys have to find a new set of "Triplets."
The new "Triplets" must involve Murray and, at some point, Lee, the talented inside linebacker who has bonded with the young running back.
"I have high standards," Murray said. "No one sets the bar higher than me. I have high standards for myself. I love this game. I am going to do everything I can do to help this team."
For the Cowboys, that means avoiding inconsistent play and physical issues.
For Murray, it means becoming an elite back.