"Andrew Cox a bit over a month ago stood in the middle of the field with all players and all staff and told us we are 100 per cent safe, no matter what we hear or read," Turinui said.
"He said he'd never sell this club to have it closed down.
"On the back of that we beat the Brumbies but then the rumours came back and the players have been dealing with it and it's just debilitating for them."
Turinui said players couldn't renew leases or enrol children at school while there was also the financial impact for all at club including staff that they could be jobless.
"How the ARU is handling it is an absolute disgrace," Turinui said.
"We have genuine issues and worries with our players and we've been pretty focused that their well-being is paramount and this has made that situation really hard for our guys.
"The ARU are putting them in a situation that puts them under extreme stress; it's not acceptable."
With the Rebels pursuing their legal options against the ARU, Cox said on Tuesday he was unable to comment and he just wanted to players to try to concentrate on Sunday's game against the Waratahs.
Cox has been heartened by the support of the Victorian government, which has gone into bat to save the Melbourne club.
A former board member of RUPA, Turinui said it needed to do more to represent the players.
"RUPA have been non-existent," he said.
"They've put out a petition on social media and said 'let's keep five teams' but they've got 40 per cent of their members under extreme duress and extreme risk of 20 per cent of them losing their job so RUPA need to step up."
The Rebels' best player, Sean McMahon, has been linked with move to Japan and while that's not entirely Super Rugby related, with the ARU not matching the overseas money, Turinui said their current situation wouldn't be helping.
He predicted more players would follow McMahon out the door if the Rebels weren't soon guaranteed a future by the ARU.
"It certainly wouldn't have helped having less than perfect certainty about the club that gave him his opportunity," Turinui said.
"I can't see how it couldn't be a factor."Turinui said Australian rugby needed Melbourne if it had any designs on being a national game, particularly given the population and economic significance of the city.
"If rugby leaves Victoria it will never come back," he said.
"If your job on the ARU board is to be the custodian of the game Australia-wide then it's gross negligence to not continue to have a presence in Melbourne."
- AAP