The "Wild Boars" team were stuck in the cave in northern Thailand for 18 days before Thai Navy SEALs and international cave diving experts successfully removed them in a highly risky, three-day-long operation.
Anaesthetist Richard Harris and his diving partner Craig Challen, both cave diving specialists, played key roles in the rescue.
Their participation came after negotiations between Australian and Thai authorities accorded them diplomatic immunity to protect them from possible prosecution if anything went awry during the treacherous mission, ABC reported, citing an official source.
Australia's foreign affairs department declined to confirm or deny the report, referring questions about the planning and implementation of the rescue to Thai officials.
The mission was "absolutely life and death" and the cave diving specialists were uncertain if they would be able to successfully save all 12 boys and their coach, Challen told local media after returning home.
"It wasn't dangerous for us, but I can't emphasise enough how dangerous it was for the kids," he told Perth's Sunday Times.
The children were sedated to the point that "they didn't know what was going on" to prevent them from panicking as they were led by the divers along the tight corridors, Challen added.
"They had drugs. We could not have panicking kids in there, they would have killed themselves and possibly killed the rescuer as well." The divers said they trained above ground with local children at a nearby pool, before practising with the trapped.boys by getting them used to donning wetsuits, buoyancy jackets and full-face masks.
Navigating through one narrow section of the tunnel in pitch darkness was particularly challenging, British diver Jason Mallinson told the ABC.
"The only time you find out about (the section) is when your head bangs against the wall," he said, describing his efforts to squeeze one boy he was rescuing through each obstacle.
"I was confident of getting the kid out. I wasn't 100 per cent confident of getting him out alive.
"Because if we bashed him against a rock too hard and it dislodged that mask and flooded his mask, he was a goner... We didn't have a backup device for them. It was that mask or nothing."
Doctors say the boys, who are recovering in hospital after their extraction last week, are in good health.
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