I was wondering about the genitive case here as well. I found an explanation here: http://blogs.transparent.com/russian/accusative-and-genitive-in-negative-russian-sentences/
I've done a small bit of research on the topic of negation in Russian, and it seems to be a really difficult topic, when you get away from the obvious нет [genitive]. I like Peatsickle's explanation about direct objects of negated verbs being cast in genitive, but I'm not sure if that can be a "rule". It seems more complicated than that.