On a tumultuous Wednesday at the Rabbitohs' training centre in Maroubra, Demetriou was forced to dismiss claims that Mitchell and Walker ran the club after Burgess resigned from his role.
Burgess, who was brought back to the club as an assistant coach earlier this year, is believed to have raised concerns with Demetriou about the preferential treatment afforded to Mitchell and Walker.
Players are also understood to have taken issue with the coach's handling of his star fullback and five-eighth.
"Latrell is a big presence as Sam was when he was playing, but to say that he (Mitchell) is dominating the club ... he's a part of the leadership team," said Demetriou, who fronted media alongside chief executive Blake Solly.
"Cameron Murray is our captain and does a fantastic job as a leader in this club.
"Is he (Mitchell) dominating the club? No, it's a comment that's ridiculous. He was out for three months, who was dominating the club then?
"One minute, (everyone) was saying we're too soft on him and, and they're running the club. And the next minute, it's, I'm falling out with everyone. So which one is it?"
Publicly Souths have claimed Burgess has stepped away from the club due to the impending birth of his child with partner, Lucy Graham, who whisked him away from the club's HQ shortly after 9am.
Burgess, who was due to leave at the end of this season to take up a role with Super League side Warrington, declined to comment on Wednesday.
He later released a statement that said it was the right time to leave "given the circumstances".
But Burgess' decision to quit the Bunnies so close to the final round of the season has raised eyebrows given his heroics for the club en route to their drought-breaking premiership in 2014 and his tight bond with co-owner Russell Crowe.
Demetriou has now lost one of the club's most-respected figures with their season in the balance.
South Sydney have a bye this week but must beat bitter rivals the Sydney Roosters next Friday to guarantee they don't miss the finals for the first time since 2017.
Mitchell will be unavailable for that clash after being handed a one-game suspension following last Sunday's loss to Newcastle.
The Australia international has struggled to recapture his form since injuring his calf on State of Origin duty and missing 12 weeks of the club's campaign.
The fullback's efforts were questioned after an anaemic performance against the Knights which was only compounded by vision of him downing beers on stage with country singer Luke Combs earlier in the week.
"Half the NRL was probably at the Luke Combs concert," Demetriou retorted.
"He slugged a few shots of beer and threw the can in the air, but he was the first bloke in the building on Thursday morning - he trained to house down.
"He drives the standards inside these four walls."
Meanwhile, John Morris has been retained as an assistant until the end of the year and led training with Demetriou on Wednesday.
Morris was reportedly close to following Burgess out the door and is expected to leave the club at the end of the season to work under Benji Marshall at Wests Tigers.
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