Huh? Game theory is the study of strategy. It's not attempting to describe how people actually behave, but how they should behave if they want to achieve a specific outcome when interacting with other people.
Some games, like second price auctions (under certain assumptions about people's values for the good, and knowledge of their own and other people's values) have so called dominant strategy equalibria. In this case, you can say how a person should act regardless of how others act.
But these scenarios are the exception rather than the rule.
It seems a bit silly to observe some behavior in a game and say "See that's a Nash Equilibrium, so game theory works", and then to turn around and observe some non-NE behavior and say "well in this game, BNE is clearly the right model, so game theory still works". And then yet again to observe some more behavior that conflicts with the theory (or to get rid of silly equilibrium) and say "ah, now we simply use perfect Bayes" or trembling hand equilibrium, or actually we were totally using correlated equilibrium this whole time.
In any case, it feels weird that a theory should behave like the "No true Scotsman" fallacy. We can always get the equilibrium by simply redefining what we mean by equilibrium.
And I think in the cases where the NE are predictive of actual play, then there's something intuitively obvious about the NE, and that you could have arrived at the same conclusions without using the tools and machinery of game theory. This is the point that Ariel Rubenstein makes (http://arielrubinstein.tau.ac.il/papers/74.pdf) when he says that game theory is useless.
That's not to say that I believe that game theory is never useful (for certain limited settings, like repeated auctions, it works well), nor do I think that it can never be useful (recent work in behavioral game theory is promising in my opinion) but I'm skeptical using these counterintuitive claims as examples of its use.