Twice today (and many times past) I have run across people begging the question that Tomb of Horrors is a typical example of the Gygaxian GMing style. It seems to be "common knowledge" that Gygax was an adversarial GM who forced his players to learn a dungeon's tricks through lethal trial-and-error which killed countless characters, and who placed little-to-no emphasis on story or role-play.
And every time I ask for details, Tomb of Horrors is the example given.
I've also heard--from much less vocal sources--that Tomb of Horrors is pretty far afield from Gygax's typical approach. They say it was especially designed for exceptional players who requested exceptional challenges for their exceptional characters, but the details always vary: he wrote ToH to challenge a particular group of friends who felt invincible, or he wrote it to refute an accusation that he ran "fluffy" adventures because he couldn't do anything harder, and so forth.
So, what's the truth? Is the Tomb of Horrors adventure typical of a session with Gygax, or is it significantly unlike his normal DMing style? If it's different, why and how? This confusion started because of apocrypha and pilgrims' notes, so please provide solid quotes and sources to back up your answers!