The rule clearly states that a player being put on injured reserve must have suffered an injury that would sideline him for at least six weeks. That might be tough to argue for the Packers as Rodgers was able to play in a game two days earlier and seemingly didn't get injured during it.
Written rules are subject to customary practice, it seems that the league has not applied said rule to the letter. Apparently the team also received prior approval, non-issue. If the team Doc maintains that the injury creates an enhanced risk of additional injury for say 6 weeks then its unlikely that the league would bother challenging the transaction.