Steven and most of the people here (including me) do indeed believe that "you are your brain" in the sense that the mind is something that the brain does. But Steven's epigram is using "you" in a narrower sense, referring to just the conscious, internal-monologue part of the mind.

In the fable of the fox and the grapes, it's the fox's brain that is the proximate cause of him giving up the attempt to get the grapes, but it's the "creepy vizier" part of his mind that makes up the "I didn't want them anyway" story.

(Edit: I should have said "most of the other people here" in my first sentence. In case you didn't know it, Steven Kaas is an LWer. He is kind enough to let me and others earn tons of karma by quoting his Twitter bons mots.)