Triple Eight has been at odds with Supercars and Burgess since the Saturday evening of the season-opening Newcastle 500 earlier this month.
It was at that point the two T8 Camaros were stripped of their one-two finish in Race 1 thanks to the placement of a dry ice radiator on the driver's side of the cars.
While not allowed under the technical regulations, T8 argued that it had sought and received approval from Burgess to run the system as fitted to aid driver cooling.
Burgess later denied that in a post-race hearing which led to the cars being disqualified from the race.
A furious Jamie Whincup, T8 managing director, slammed Supercars over its treatment from the series.
A subsequent appeal hearing last week reached the same conclusion as the original hearing, with Burgess again denying that he had given T8 approval for the placement of the dry ice system.
T8 responded to the disqualification being upheld by once again stating that it approval had been given.
Asked by Motorsport.com at Albert Park to respond to what are effectively allegations that Burgess wasn't being truthful at either hearing, Supercars CEO Shane Howard said: "We completely disagree with that.
"Obviously that would be clear in the hearing. There is a lot of emotion in and around it. Was Adrian asked for approval? No, he wasn't. Formally he wasn't asked for approval, and he didn't grant it.
"Now, there were discussions around conversations or misinterpretations, but I believe it was pretty clear. The decision has been made and we move on."
Censorship of criticism has been a key topic in Supercars recently following a protest from Shane van Gisbergen following the second Newcastle race.
He refused to answer media questions in full, citing pressure from "top brass" at Supercars to not criticise the new Gen3 cars.
That it not believed to have come from Supercars management directly, with Howard saying even Whincup's comments about T8's treatment from Supercars wasn't worthy of bringing the sport into disrepute.
"When you're in a situation like that there's a lot of emotion and people can say things that they probably could regret later," said Howard.
"Jamie and I have discussed it post [appeal], and we agreed that the decision has been made and we move on."
