BF Skinner would have said: There is only behavior. Behavior is shaped by the environment. Thinking, speaking, and explaining are nothing but a special kind of behavior. Thus it is perfectly possible to be proficient at walking down stairs without being able to explain how exactly it is that you are doing it. In the same way, someone might be very proficient at explaining how to play tennis, without actually being able to hit a ball. these are just two very different kinds of behavior.
I find your comment suprising. If by "explain" you mean "being able to control and predict", I would say that Skinner explains a helluvalot of the modern world, doesn't he? Facebook, Twitter, and even Hacker News work on positive reinforcement. One could argue that this has become one of the most dominant forces in our culture, spanning from advertising to politics.
I get that Skinner stopped being "cool" in the 70s when Chomsky et al appeared. But I have yet to see a Chomsky train a pigeon to play ping pong.
How do you think he was wrong? What model do you believe explains things better?
I don't see how Skinner could be wrong unless you reject materialism. Everything reduces to the behaviour of particles in the end. Of course it's possible that behaviour is not an effective way to model and study human beings, just like using particle physics is not an effective way to study English literature, but there's little doubt that English literature reduces to particle physics in the end.
Sure, if you stretch the meaning of "behavior" far enough, that quote is true because it becomes a tautology.
However, Skinner had some pretty specific ideas about what "behavior" meant and probably wouldn't have included stuff like playing a chess game against oneself in one's head.