Cricket Australia (CA) ruled captain Pat Cummins out of the Adelaide Test before he was officially deemed a close contact of a COVID case.
But CA says it was acting on inside information from emergency meetings with South Australian Health in withdrawing Cummins from the second Test against England.
South Australian Premier Steven Marshall says Cummins was ruled out on Thursday morning before he was interviewed by health officials.
"This is a decision that was made by Cricket Australia, let's be very clear about it," Marshall told reporters on Friday.
"They put their statement out before we actually conducted the interview with Pat.
"So the issue is that Cricket Australia probably formed the opinion that they didn't want to have a chance for the entire two teams to be deemed as close contacts and ruin the entire Test series."
CA issued a statement three hours before the start of Thursday's play saying SA Health had confirmed Cummins "is a close contact and will be required to isolate for seven days".
The Test skipper was at a steakhouse on Wednesday night when another patron in the same indoor area as Cummins was notified he had COVID.
Fellow Test bowlers Nathan Lyon and Mitchell Starc were at the same restaurant at the time but were seated outdoors and not considered as close contacts.
CA chief executive Nick Hockley said SA Health had confirmed Cummins would be classed as a close contact when it made the decision to withdraw him from playing.
"We called an emergency meeting with our contacts at SA Health and they confirmed to us that Pat would be treated as a close contact," Hockley told SEN radio on Friday.
Hockley ruled out putting players into lockdown when the five-Test series moved to Melbourne and Sydney, cities where COVID case numbers are higher than Adelaide and Hobart, the venue for the fifth Test.
Players would still be allowed to attend restaurants in small groups in Melbourne and Sydney - if they dined outdoors.
"If players are keeping themselves to small groups and they're interacting with their own group only, they're trying to keep away from indoor settings, then we think with masks and regular testing we can mitigate," Hockley said.
"It's a wake-up call for everyone across the game.
"We are confident in our protocols that they're appropriate and it is that fine balance about common sense.
"Everyone now just needs to be extra vigilant because we have had a real very high-profile case of disruption."
The fresh comments came after Australian batsman David Warner said was inevitable more players will become close contacts of COVID-19 cases.
"It's inevitable in today's society that people are going to get COVID or become close contacts," Warner said after Thursday's play.
"Unfortunately, Pat was in a spot where someone had tested positive that day."
Warner said Australian players had been told not to go out in groups bigger than three and to try to avoid busy places such restaurants and cafes.
