Skinner conflates internal mental theory with any internal theory at all. Inference about the causal basis of the data. Introspection doesn't get you out of scientific trouble, it gets you into it. But reinforcement doesn't get you out of it either. Only a causal theory of behavioural capacity will.
Neural activity is surely the basis of both behavioural capacity and mental states.
To explain the latter, it must first explain the former. But what is needed is not neural DATA, any more than we need behavioural data. Skinner speaks of learning as if it were an internalist inference of the kind he would eschew. But of course it is just an empty term, hence harmless for him. But for that, working hypotheses are needed, and those are not forthcoming from behaviorism.