But in a statement, European Rugby Cup said Thomas upheld the citing complaint and found that Hines had “stamped on his opponent and had connected on more than one occasion”.
Thomas decided the offence warranted a mid-range entry point of a five-week suspension, but he added a week due to 35-year-old Hines' poor disciplinary record.
He will miss Clermont's Heineken Cup trip to Exeter on Saturday, and cannot play again until November 26, although he will be available for Clermont's crunch Pool Five clashes against holders Leinster in December.
Hines won 77 Scotland caps before calling time on his international career last year. He also toured South Africa with the 2009 British and Irish Lions.
Wales international Stoddart, meanwhile, has been cleared to continue playing following his sending-off against Clermont.
Stoddart was shown an automatic red card by Irish referee Peter Fitzgibbon after receiving two yellows in a game his team lost 49-16 at Stade Marcel Michelin.
But ERC independent judicial officer Anthony Davies, who considered the matter by means of written submissions, decided the red card was sufficient punishment, tournament organisers announced.
Davies concluded that neither yellow card offence involved foul play directed at an opponent and that no additional action was necessary.
It means that Stoddart is available for the Scarlets' Heineken Cup appointment at home to Leinster on Saturday.
Glasgow wing Tommy Seymour, though, has been banned for a week and will miss his team's Heineken encounter against Ulster tomorrow night.
Seymour was cited by match commissioner Yves Thieffine for a dangerous 'tip' tackle on Northampton's Vasily Artemyev during a Pool Four fixture last Sunday.
He pleaded not guilty to foul play at a disciplinary hearing in Dublin, but Thomas upheld the citing complaint.
ERC said: “The judicial officer upheld the citing complaint and employing the IRB recommended sanctions for Law 10.4(j), he decided that the offence warranted a low-end entry point of four weeks.
“However, when considering the very specific circumstances of the tackle, the judicial officer felt that a four-week suspension would be 'wholly disproportionate'.
“Accordingly, and based on the presence of a number of mitigating factors, including Seymour's clean record, the judicial officer reduced the sanction to a one-week suspension.”