I think you have a different understanding of what exactly a brand is than do most people. Every profession has the right to develop its own jargon that subtly redefines common words in its own way so I'm not going to say that you're wrong about what "brand" means in any absolute way, just that you're wrong to say that pg is wrong.
Fair enough - although I'd add in my defense that my take wasn't "Paul Graham is wrong", in fact I really liked the essay and agreed with a lot of it. It was more that I think there's a lot more going on with brands than the essay makes out (although you might disagree with this take too)