That's . . . not quite the case either, honestly.
Early 3rd Edition DID have Greyhawk as it's core setting. Yes, it fiddled with a few details, and presented it much like they are presenting the core setting for 4e, but Greyhawk was the default setting . . . at first.
But this didn't last long (don't really recall when the turning point was). Eventually 3rd Edition morphed into exactly what you describe, a generic, nameless fantasy core setting with elements lifted from Greyhawk . . . not all that different from today's core setting for 4e, actually!