You are correct that my comments are missing the mark. Still, there is a sense in which the kinds of non-determinism represented by Born probabilities present problems for Si.
They would represent problems for determinism - if they were "real" probabailities. However the idea around here is that probabilities are in the mind.
Here is E T Jaynes on the topic:
It is a commonly heard statement that probabilities calculated within a pure state have a different character than the probabilities with which different pure states appear in a mixture, or density matrix. As Pauli put it, the former represents "Eine prinzipielle Unbestimmtheit, nicht nur Unbekanntheit" *. But this viewpoint leads to so many paradoxes and mysteries that we explore the consequences of the unified view, that all probability signifies only incomplete human information.
[*] Translation: "A fundamental uncertainty, not only obscurity"
You're about to flip a quantum coin a million times (these days you can even do it on the internet). What's your estimate of the K-complexity of the resulting string, conditional on everything else you've observed in your life so far? The Born rule, combined with the usual counting argument, implies you should say "about 1 million". The universal prior implies you should say "substantially less than 1 million". Which will it be?
EDIT: Wei Dai's comment explains why this post is wrong.