Although Russian is a logical, rule-bound language (unlike English, a chaotic, non-rule bound language), there are some cases in which native speakers deviate from the rules, and since they are native speakers, they usually can't explain the rationale for the deviation.
So...Yes, generally negative statements are followed by the genitive case (except of course with verbs such as помогать that don't govern the accusative case). Except when they don't. Insofar as one can generalize about this, specific negative statements may govern the accusative, while generalizations are more likely to govern the genitive.
But in your example, the thing to understand is that it's not the verb that's being negated but the subject of the clause, все. Negating the subject has no implications for cases.