If the Predictor breaks sometimes, in a way dependent on the algorithm used, not on the decision made, then that's not decision-determined.

Yes, that's the mantra. But how do you unpack "dependent" and "breaks"? Dependent with respect to what alternatives (and how to think of those alternatives)? More importantly, how can you decide that something dependent on one thing doesn't depend on some other thing (while some uncertainty remains)?

As far as I can tell, all this dependence business has to be about resolution of logical uncertainty. You work with concepts, say A and B, that define the subject matter without giving you full understanding of their meaning, implications of the definitions. A depends on B when assuming an additional fact about B allows to infer something about A. By controlling B, you control A, and similarly if you find a C that controls B, you can control A through controlling C. All throughout, nothing is actually changed, the concepts are fixed.

If you know that A depends on B, and there's also some C, then unless assuming full knowledge of B allows you to obtain full knowledge of A, you won't be able to conclude that A is truly independent on C (screened off by B). If you are merely unable to see how knowing C can allow learning more about A, doesn't prohibit the possibility of figuring out a way later, and that would mean that C controls A after all.

So we can talk about action-determined outcomes and decision-determined outcomes, where the concepts of an action, or of a decision, are in known dependence with an outcome. But arguing that the outcome doesn't depend on given other concept is much more difficult, and more of impossible if you are dealing with sufficiently complicated uncertainty.