According to Channel Nine, officials tried to cover up Warner's pub fight with England batsman Joe Root in Birmingham's Walkabout bar in the early hours of Sunday morning.
Former vice-captain Watson, one of four players dropped for a Test against India in March after failing to respond to Arthur's demands for suggestions on how the team could improve, reportedly accused the South African of double standards.
The report suggested Watson's complaint led to Warner being fined and suspended until the Ashes, but Clarke denied the all-rounder approached Arthur.
"He certainly didn't. It's irrelevant I guess firstly how the leadership group found out about the incident," the Australia captain said after training at The Oval on Friday.
"And, no, Shane certainly didn't take up with Mickey that he had a problem with how we as a leadership group dealt with it. That allegation is completely false."
Pressed on whether Watson - who no longer has any involvement with the leadership group - was disappointed or felt hard done by, Clarke said that was for the 31-year-old to answer.
Clarke said Watson and the Australia squad were disappointed in Warner's actions, which Cricket Australia chief executive James Sutherland described as 'despicable' on Friday.
"I think all the players are disappointed with David's behaviour. Everybody acknowledges he's let the team down - there's no doubt about it," he said.
"I don't think Shane's in a different situation to any of the other players."
The skipper, who is battling a back injury, said the seriousness of the Walkabout incident had not been underestimated.
Clarke criticised the players for being out drinking after their loss to England at the ICC Champions Trophy on Saturday.
"I think what James has certainly said, and I will echo, after losing a game like we did against England, to be out at that hour celebrating or carrying on like we were celebrating, especially with the opposition, is probably not the right time or place to be having a few drinks," he said.
"Every player is aware of that. I think everything in moderation.
"A big part of why you loving playing cricket for Australia is because you celebrate your success, you work hard together as a team, but when you do well you do celebrate together, but you need to have a reason to celebrate and right now we certainly haven't got that."