Economic game theory's "folk theorem" is not empirically relevant

I study a lot of game dynamics: how people learn as they make the same socially-inflected decision over and over. A branch of my career has been devoted to finding out that people do neat unexpected things that are totally unpredicted by established models. Like in most things, anything close to opposition to this work looks less like resistance and more like indifference. One concrete reason, in my area, is that it is old news that strange things can happen in repeated games. That is thanks to the venerated folk theorem. As Fisher (89) put it, the “folk theorem” is as follows

in an infinitely repeated game with low enough discount rates, any outcome that is individually rational can turn out to be a Nash equilibrium (Fudenberg and Maskin, 1986). Crudely put: anything that one might imagine as sensible can turn out to be the answer

It is a mathematical result, a result about formal systems. And it is used to say that, in the real world, anything goes in the domain of repeated games. But it can’t be wrong: no matter what one finds in the real world, a game theorist could say “Ah yes, the folk theorem said that could happen.” What’s that mean for me? Good news. The folk theorem, as much as we love it, is fine logic, but it isn’t science. It says a lot about system of equations, but because it can’t be falsified, it has nothing to offer the empirical study of human behavior.
Oh, FYI, I’d love to be wrong here. If you can find a way to falsify the Folk Theorem, let me know. Alternatively, I’d love to find a citation that says this better than I do here.
Fisher F.M. (1989). Games Economists Play: A Noncooperative View, The RAND Journal of Economics, 20 (1) 113. DOI:

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