This is something that struck me odd when reading something in a different post...
First, read what I'm about to say, keeping in mind the information Dumbledore and the wizarding community had 15 years ago, not what is probably common knowledge now.
The Wizarding Community believes: Sirius betrayed James and Lily Potter's whereabouts to Voldemort, who goes and kills them. Wormtail tracks him down and, heartbroken over the betrayal of two friends by another friend, tries to dual with Sirius. Sirius kills Wormtail and 12 Muggles. The only bit ever found of Wormtail was a finger.
keep in mind, now, that Dumbledore knows Wormtail, not Sirius, was the secret-keeper
Dumbledore believes, before the past 3 books: Wormtail betrayed James and Lily Potter's wherabouts to Voldemort, who goes and kills them. Sirius tracks down Wormtail, who falsely accuses Sirius of betraying James and Lily and, heartbroken over the betrayal of two friends by another friend, duals and comes of the best with Wormtail. Sirius kills Wormtail and 12 Muggles. The only bit ever found of Wormtail was a finger.
This is the only reason I can see that Dumbledore wouldn't have stepped up at some point and said that Sirius wasn't the one who betrayed James and Lily, it was Wormtail. However, he does believe that Sirius killed Wormtail and 12 innocent Muggles afterwards, and Sirius needs to be convicted and sent to Azkaban for those deaths, so he just doesn't bother bringing up the fact that Sirius didn't betray the Potters, because he still thinks he needs to be punished for the deaths he was responsible for... ????????