Inhabitants of a Hume world are right to explain their world with this Hume-world theory. They just happen to live in a world where no prediction is possible.

Just because what you believe happens to be true, doesn't mean you're right to believe it. If I walk up to a roulette wheel, certain that the ball will land on black, and it does--then I still wasn't right to believe it would.

Hypothetical Hume-worlders, like us, do not have the luxury of access to reality's "source code": they have not been informed that they exist in a hypothetical Hume-world, any more than we can know the "true nature" of our world. Their Hume-world theory, like yours, cannot be based on reading reality's source code; the only way to justify Hume-world theory is by demonstrating that it makes accurate predictions.

Arguably, it does make at least one prediction: that any causal model of reality will eventually break down. This prediction, to put it mildly, does not hold up well to our investigation of our universe.

Alternatively, you could assert that if all possibilities are randomly realized, we might (with infinitesimal probability) be living in a world that just happened to exactly resemble a causal world. But without evidence to support such a belief, you would not be right to believe it, even if it turns out to be true. Not to mention that, as others have mentioned in this thread, unfalsifiable theories are a waste of valuable mental real estate.