I disagree with that. I love sword and sorcery and REH stands as one of my hands down favorite authors but I just do not find Greyhawk relevant to what I want to run or play in.
So no just because you have zero interest in Greyhawk does not mean you dislike the works of such folks as REH Camp & Pratt,Fritz Leiber or E.R.Burrough.
Maybe you do not feel GH captures the feel of sword and sorcery. But is uninspiring to you. Maybe it just does not feel like something Burrough or REH would write to you.
So no Greyhawk is not the be all end all of sword and sorcery roleplaying.
You've gotten the conditional statement wrong. The claim is not that if you like S&S, then you'll like GH. That would imply that if you don't like GH, then you don't like S&S. That's the thing that you're saying is wrong, and I agree with you. But it's not the claim being made.
The claim is that if you do not like S&S, then you won't like GH. Perhaps you also take issue with that claim, but it's not the same thing. It in no way implies that GH is all there is to S&S. But it does imply that GH one of many things found in the S&S genre.
The funny thing is, Philosopher, that quote is going in the opposite direction. It's anti-realism. Gary is chiding wargamers who prefer their games to be historically accurate, without wizards and dragons and elves, saying they lack imagination.
Indeed many gamers might feel that Greyhawk is too unreal for their tastes, with all of the crazy stuff - the D&D wandering monster tables with added monsters for example. Sure it's more real if you compare it to Forgotten Realms, World of Warcraft or some anime, but that's not saying much. Like I mentioned upthread, when I played in a Greyhawk game, the main modification the GM made was to cut out a lot of the D&D zoo.
The claim is that GH is in the S&S genre, not that it is "realistic", so I'm not sure what you mean when you say the quote is "going in the opposite direction". Do you mean that Gygax's point is that D&D is about fantasy rather than being specifically about S&S? If so, that's a fair point. But I think the examples he uses are telling.
Indeed, partly because of that zoo, Greyhawk doesn't really resemble Hyboria, Lankhmar or even, I think, Barsoom. It's way more of a kitchen sink setting than any of those, mostly because it's default D&D, which is:
a) A crazy zoo of monsters and magic.
b) Its own genre.
The only fictional fantasy world I'm familiar with that gets close to the monster and magic heaviness of Greyhawk is Vance's Dying Earth. And the worlds of Marvel and DC, if you count them as fantasy.
D&D's not medieval. It's the Wild West with swords and plate mail. It pulls in stuff from all over - Caine from Kung Fu, Celtic bards and druids, Vancian wizards, knight hospitallers with Biblical powers, Conan, Cugel the Clever, Fafhrd & the Gray Mouser, demi-humans from Tolkien. These guys, all together in the same hodgepodge of a world, enter a very big hole in the ground to fight a zoo of monsters from mythology, folklore, sci-fi, Hammer horror movies, HP Lovecraft, kids' toys and Gary's fevered imagination.
And this is all true of Greyhawk. It's a big old mess.
I guess I had something specific in mind about what S&S is. I'm not sure if I want to get into that issue, as it's a whole other can of worms.

All I'll say is that S&S is rather multifarious, and I do think GH is included, whereas FR and DL are not. When you said, "It's the Wild West with swords and plate mail. It pulls in stuff from all over - Caine from Kung Fu, Celtic bards and druids, Vancian wizards, knight hospitallers with Biblical powers, Conan, Cugel the Clever, Fafhrd & the Gray Mouser, demi-humans from Tolkien," I have to admit that (perhaps with the exception of Tolkien) this sounds like it would fit perfectly into the S&S genre - high action with no single metaplot. Howard's Conan tales, Leiber's Fafhrd and Grey Mouser tales, Moorcock's Elric tales - they've got a bit of that kitchen sink thing going on (although, granted that it's not quite as much as GH).
I would argue that GH
was default D&D, but is not anymore, and hasn't been for quite some time (despite WotC's claim about 3e). As I said in my last post, I think D&D has evolved much since those early days. So has GH, but not as much. Calling GH "a big old mess" is fairly apt, but either I don't think it's as much of a mess as you do, or I have more tolerance (fondness?) for messes than you.