*forgets the entire conversation between Harry & Remus about why he was fired and replaces it with this* HEADCANON OFFICIALLY ACCEPTED!<<he never said he was fired. He said he resigned, but for a different reason
"Of course it is happening inside your head, Harry, but why on Earth should that mean that it is not real?" - Albus Dumbledore, _Harry Potter and the Deathly Hallows_ Make your dreams that are good a reality.
I think the reason people don't make the connection (I have a hard time myself) is that we don't see them as a group for more than a few seconds and Peter doesn't come in too much as part of the gang. We know him so much more as the Betrayer