Your pie is made of Schrodinger Apples, and whether or not they are "fresh" remains, as far as I know, a question very much up for grabs, among physicists and metaphysicists alike. And possibly futile.
But I'm not sure your question needs to bring in QM at all. Argument from an "absence of knowledge" is indeed an element of induction and a crucial assumption of science.
The argument that everything or, indeed, anything is "causally determined"is a claim of complete knowledge. Some Laplace machine can work out every possibility, with no room for randomness, "clinamen," or miraculous intervention. Modern science (since statistical thermodynamics) never makes such absolute claims (no matter what individual scientists may say).
Thus the demonstration of a "lack of knowledge" does indeed "disprove" not any particular theory, but any claim that the theory implies concerning "complete knowledge." Thus the inductive compromise. The theory is "true for now," until its direct predictions are falsified. But it can never claim "complete knowledge," even internally, and is thus validly limited by any and all claims of "incomplete knowledge."
As an aside, the whole acceptance of "lack of knowledge" is central to the modern project. A good example is the way in which ancient maps were always filled up with fanciful dragons, chimera, netherworlds, and whatnot. It was only with modern exploration that maps became marked "Unexplored," thus inviting empirical research. This is the cartographic innovation comparable to Kant's noumena. Until the "lack of knowledge" is admitted as a limit into the arguments, we have the futile contentions of a prior assertions.
How many of today's QM arguments fall into this realm of futile antinomy remains to be seen. Hidden variables may turn up. Or we may find that we act like Berkeley's God, splitting universes or endowing states-of-affairs with existence by what we now innocently call "observation."
