The problem with that theory is that Dumbledore didn't know until Harry's third year at school that Pettigrew, not Sirius, was the Potters' secret keeper. No one had told him of the switch before then. Had he have known that can you imagine him being willing to let Black stay in Azkaban for 12 years? He would have been suspicious about the allegations of Black killing 20 people as well if he knew it was Pettigrew, not Black, who was in Voldemort's service. Dumbledore would have been appealing the ministry for Black's release... just as he tried to do for Morfin (a much less likeable character than Black) and also for Hokey the House-Elf.