I'm a little mystified as to why you brought this up in response to Mike's perfectly cogent point (though "ultraleftists and other narcissists," without elaboration, sounds like strawman building to me), and why pithy formulations like this would be thought to represent the definitive word on some group's politics, especially when in situations like the occupations that group has to interact with a multitude of other groups. I've probably said this enough to get annoying--I know it is to me--but people's politics can't be reduced to their verbal declarations.
But still, Graeber's formulation is bad. Some words that come before it, in Fragments of an Anarchist Anthropology:
"Anarchists like to distinguish themselves by what they do, and how they organize themselves to go about doing it. And indeed this has always been what anarchists have spent most of their time thinking and arguing about. Anarchists have never been much interested in the kinds of broad strategic or philosophical questions that have historically preoccupied Marxists—questions like: Are the peasants a potentially revolutionary class? (Anarchists consider this something for the peasants to decide.) What is the nature of the commodity form? Rather, they tend to argue with each other about what is the truly democratic way to go about a meeting, at what point organization stops being empowering and starts squelching individual freedom. Or, alternately, about the ethics of opposing power"
There's lots to object to here, but most striking to me is the fact that any sort of antagonism is erased in Graeber's definition of anarchism; apparently, anarchists don't fight against the commodity form or against value creation, for example. In this telling, anarchists just, you know, hang out and create new forms of ethical life, magically undisturbed by capital and the state.
Graeber's objection to demands has a similar character: we don't want to legitimize the state by asking anything of it. Well, guess what, the state could care less if you think it's legitimate or not; it doesn't need your imprimatur to continue functioning. There's lots of good stuff to be said about "independent" forms of organizing, about shaping new kinds of "counterpower" and prefigurative forms of life, and about short-circuiting the state by sidestepping it instead of opposition to it, but when it forsakes structural antagonism for the pure and the ethical, it really does become what Bookchin feared it would be.
Luckily, Graeber's practice of anarchism is light years beyond his theory of it.