Right. To quote myself:

P(outcome | do(action)) has no proper place in our agent's decision-making. Savages theorem requires us to use probabilities for the things that determine the outcome; if our action does not determine the outcome, its probability isn't given by Savage's theorem.

And I do think that simultaneously, we can use Cox's theorem to show that the absent-minded driver has some probability P(state | information). It's just not integrated with decision-making in the usual way - we want to obey Savage's theorem for that.

So we'll have a probability due to Cox's theorem. But for decision-making, we won't ever actually need that probability, because it's not a probability of one of the objects Savage's theorem cares about.