I made the same argument on tvtropes independently. My thought was that Sirius and Peter were human-form animagi of each other, as a wizardry analogue to getting matching tattoos. Although maybe one's choice of animagus form is involuntary: Peter was completely obsessed with Sirius at the time that the two performed the spell, but not Sirius with Peter, so Peter's form was Sirius but Sirius, to his surprise, turned into a dog instead. Maybe that's why they broke up.
I'm not sure the dementors see people the way we do: they certainly don't in canon. If Peter's mode-lock wore off in Azkaban, the dementors might not notice or care.
If Fawkes thinks that Peter is innocent, he probably is. But maybe Sirius is too. Maybe Sirius was the only one who knew that Peter was the secret-keeper, so he assumed that Peter betrayed the Potters but he'd never be able to prove it. So he switched identities and faked his own death, and remains ignorant to this day that Voldemort doesn't need a traitor to find his victims.
- This thread has run its course. You will find newer threads in the discussion section.
Another discussion thread - the fourth - has reached the (arbitrary?) 500 comments threshold, so it's time for a new thread for Eliezer Yudkowsky's widely-praised Harry Potter fanfic.
Most of the paratext and fan-made resources are listed on Mr. LessWrong's author page. There is also AdeleneDawner's collection of most of the previously-published Author's Notes.
Older threads: one, two, three, four. By tag.
Newer threads are in the Discussion section, starting from Part 6.
Spoiler policy as suggested by Unnamed and approved by Eliezer, me, and at least three other upmodders:
It would also be quite sensible and welcome to continue the practice of declaring at the top of your post which chapters you are about to discuss, especially for newly-published ones, so that people who haven't yet seen them can stop reading in time.