I think (I would have to reread it more carefully) is Parisi's argument is that probabilistic models can sometimes be necessary even with deterministic systems that are well-characterized because the systems are extremely sensitive to information that might be difficult to obtained (i.e., measure).

I think compression/algorithmic complexity frameworks are relevant in that they imply in complex systems deterministic-like prediction with very narrow posteriors will require larger and larger computational resources. Ie the concentration of the predictive posterior depends on the computational resources available.