I think that the comic takes place after the game, not before. The GBs are already acquainted with Peck as the head of the Oversight department in the normal comic story, it's only in the second "Paranormal Files" stories do we see how it happened. It's his "origin" story pretty much.
Also, we have those guys playing pool who talk about how the GBs have been a franchise for a while and they want to get in on it. That doesn't sound like they just got turned into a paid-for-by-the-city service.