If belief is construed as some sort of representation which stands for external reality (as in the case of some correspondence theories of truth), then we can take the claim to be strong prediction of contemporary neuroscience. Ditto for whether we can explain why we talk about qualia.

It's not that I could explain exactly why you in particular talk about qualia. It's that we have an established paradigm for explaining it.

It's similar in the respect that we have an established paradigm for explaining why people report being able to see color. We can model the eye, and the visual cortex, and we have some idea of what neurons do even though we lack the specific information about how the whole thing fits together. And we could imagine that in the limit of perfect neuroscience, we could synthesize this information to trace back the reason why you said a particular thing.

Since we do not have perfect neuroscience, the best analogy would be analyzing the 'beliefs' and predictions of an artificial neural network. If you asked me, "Why does this ANN predict that this image is a 5 with 98% probability" it would be difficult to say exactly why, even with full access to the neural network parameters.

However, we know that unless our conception of neural networks is completely incorrect, in principle we could trace exactly why the neural network made that judgement, including the exact steps that caused the neural network to have the parameters that it has in the first place. And we know that such an explanation requires only the components which make up the ANN, and not any conscious or phenomenal properties.