That's why when I want lists of GH gods I use GH materials - the boxed set, From the Ashes, the later 90s stuff, and the Living Greyhawk Gazetteer.Some of those prior online lists of Greyhawk gods for instance have the tons of expansions of gods from 3e and 3.5 sourcebooks.
I think the reason that Greyhawk was used for the Living Greyhawk game is because otherwise it would be very poorly named!They aren't derived from Greyhawk. They ARE Greyhawk. Greyhawk is the default setting, which is why it was used for the Living Greyhawk games.
I believe the word Greyhawk does not appear anywhere in the 3E PHB. It just presents the world of Dungeons & Dragons. As I've posted, when I want to understand how Boccob relates to worshippers I refer to my GH materials, not the irrelevant sideshow of the 3E DDG. (Which also does not contain the word Greyhawk.)