Yes, of course this is in conflict with not just the AFR, but with a lot of what we think we know about ourselves. And yep, I think the whole mess is self-referentially incoherent. Showing that it is, however, is more of a chore than you realize.
On the one hand, the Churchlands are committed to listening to brain science and seeing what those disciplines have to tell us about what our cognitive enterprise is like. Interestingly enough you have a lot their fello naturalists, like Jerry Fodor, who aren't looking to brain science to provide much info on what our cognitive life is like. The reason is that there seems to be too big of a disconnect between our mental life as we know it through introspection and what science is going to come up with. There are people who say, yes, in some sense it is all material, but you shouldn't be too eager to throw over huge elements of what Sellars called the Manifest Image (as opposed to the Scientific Image), because to do that is going to undercut what we know about our mental life. So I guess there's a kind of promissory note put out there that the disconnect will go away someday, but an unwillingness to turn neuroscience into philosophy.
The Churchlands are the deadly enemies of people like Fodor; they think we have to start taking neuroscience seriously now, even if it means that we start thinking that we are dead wrong about having things like propositional attitidues like belief. So they are classed as eliminative materialists, eliminativists in the sense that they say that we have to be prepared to throw over our common-sense understanding of our cognitive life. It is typical to couch their position as the claim that there are no beliefs, but actually what they suggest is that as science develops on cognition, we may have to be prepared to drop the notion of belief. We may have better terms to use once brain science gets where it will eventually go. The problem that they face is precisely what you mentioned: that when they talk about all of this they use the langauge of common sense psychology. But it's not as if they're going to hit their heads and say "I never thought of that" if you point out to them that they are using prescientific language. I mean, what other language would you suggest they use? We don't have the scientific image mapped. So they may say "if you think about it" but they may think that, if they knew enough future neuroscience, they wouldn't talk like that. They routinely hit self-referential objections with a charge of begging the question.
My contention is that the disconnect between naturalistically acceptable talk about cognition and the common-sense talk (I did the mathematical question, and concluded such-and-such) is a logical disconnect, and that any reconciliation is bound to be based on some sort of confusion of categories. For starters, surely neurons don't know, even if things composed of neurons do know. Talk about neurons making predictions seems puzzling as well. What does that mean? If I say, "I predict the Lakers will win the NBA Finals this year", that doesn't make sense unless you attribute to me all kinds of states that are naturalistically illegal.
In fact, I have identified four dimensions of our mental lives which seem to be automatically excluded from base-level naturalistic accounts: intentionality, normativity, subjectivity and purpose. The divide between something that these terms can apply to, and that which these terms cannot apply, doesn't work. And being told "Aha, look at all the nifty stuff science is discovering about the brain! Surely this great divide will someday be crossed if we keep going on brain science!" doesn't wash. It is as if a lot of nifty maps of one side of the Grand Canyon can tell us how to get across the Grand Canyon. Bridging attempts, such as functionalism, appear to work, in my view, because we take out eyes off the ball and miss the category mistakes.
But this has been battled out numerous times on Dangerous Idea 2. Haven't been over there much lately, because I haven't done a lot of AFR stuff of late. There are also some very nice BDK/Doctor Logic vs. Darek Barefoot debates that were done around late 2007, when I was writing the Blackwell Companion entry on the Argument from Reason.