Fricker on concepts and states

Elizabeth Fricker writes:

Williamson maintains that 'knows' has no analysis 'of the standard kind'—this being one that factors knowing into a conjunction of mental and non-mental components, notably the mental state of (rational) belief plus truth and some other factors. Call this thesis NASK. If NASK were false, 'know' having an a priori necessary and sufficient condition in terms of belief plus some other (non-factive) mental and non-mental components, this would establish the falsity of KMS ['knowledge is a mental state']: knowing would be revealed a priori to be a conjunctive 'metaphysically hybrid' state.

I find the suggestion that there is any deep connection between NASK (a claim about the concept 'knows') and KMS (a claim about the nature of knowledge) somewhat confusing. She characterizes the denial of this connection as an 'error theory':

Here I follow Williamson in ruling out the possibility of an error theory—that our concept 'knows' could be complex, while it in fact denotes a simple state. It is doubtful whether this is even coherent, and it can surely be discounted.

I don't see why this would be an error theory, and I don't see why it should be thought incoherent (unless one is worried about the coherence of the very notion of a complex concept, as Fricker clearly is not). It's not true in general that there's any problem with the concept of 'X' having some property, while X itself has a contrary property. (The concept 'sky' has no colour, but the sky is blue.)

So what's going on?