I think there seems to be a mismatch of terms involved. Ontological probability, or propensity, and epistemological probability, or uncertainty, are being confused. Reading over this discussion, I have seen claims that something called "chaotic randomness" is at work, where uncertainty results from chaotic systems because the results are so sensitive to initial conditions, but that's not ontological probability at all.
The claim of the paper is that all actual randomness, and thus ontological probability, is a result of quantum decoherence and recoherence in both chaotic and simple systems. Uncertainty is uninvolved, though uncertainty in chaotic systems appears to be random.
That said, I believe the hypothesis is correct simply because it is the simplest explanation for randomness I've seen.
We argue using simple models that all successful practical uses of probabilities originate in quantum fluctuations in the microscopic physical world around us, often propagated to macroscopic scales
Their argument is that not only is quantum mechanics ontologically probabilistic, but that only ontologically probabilistic things can be successfully described by probabilities. This is obviously false (not to mention that nothing has actually been shown to be ontologically probabilistic in the first place).
...Thus we claim there is no physically verified full
If it's worth saying, but not worth its own post, even in Discussion, it goes here.