Which part of Fallon's research is unsound, 1) the neurological correlation, 2) his characterization of it, or 3) the characterization of himself?
Regarding, e.g., the Hare criteria not being science, it's not true that such criteria are not testable. You're conflating accuracy (or trueness) with precision. The diagnostic criteria clearly lack precision, but they don't necessarily lack accuracy. Macroeconomics lacks precision but various theories are incredibly accurate. That said, actually rigorous testing is lacking. It's lacking partly for the reasons I specified, but lacking nonetheless. And that's fair. But experimental results are not the sine quo non of how we understand the world; it's not black & white like that. There are other modes of understanding the world, and other substantive indicia of the correctness of theories. The Scientific Method is one of the best modes and its results some of the best forms of evidence, but it's hardly exclusive.
In any event, look at the similar condition of narcissism. Like sociopathy that word gets thrown around so much it's almost meaningless in a lay context, and there are wide margins where the classification is dubious even in a medical context. When people (including experts) claim Nixon, Clinton, or Alex Baldwin are narcissists, you sort of roll your eyes because such aversions tend to expose the term for being so loose and imprecise to the point of being useless. You can't even agree or disagree.
But is there any doubt in your mind that Donald Trump is a testament to some physiological phenomenon that fits squarely within the box we label narcissist? What that classification implies regarding his fitness as president is another matter altogether, but I don't think there exists many practitioners even loosely related to the study of the human brain that don't sense he's the archetype of some concrete and identifiable human condition.