Will Bryan Caplan take the bait and present his argument that such studies are a priori false because the studies themselves rely on data from consciousness? Of course this counterargument is wrong. We can make lots of mistakes, but still hold the capacity to measure some of those mistakes.
At risk of going too far from econ for Econlog, I'll bite.
1. I would only make this specific argument from self-contradiction against someone who claimed that no mental states exist (i.e., some version of eliminative materialism), or a radical skeptic who claimed that we know nothing about mental states.
2. There are plenty of claims about mental states that I agree are fallible: Memories of mental states, empirical generalizations about mental states, even causal claims about mental states.
3. Nevertheless, there is still a solid core of claims about our mental states that we cannot be wrong about. How is that possible? Because in many cases, there is no distinction between seeming to have a mental state, and really having it. If it seems to me that I am now experiencing a sweet taste, then I ipso facto am experiencing a sweet taste. If it seems to me that I am now thinking about an elephant, then I ipso facto am thinking about an elephant. Whatever else he got wrong, Descartes got this right.
P.S. For some related readings, see here and here.