Reading the comments so far, I think Peter wasn't as clear as he had hoped (or this is all jumping to disagree too quickly). As I see it, the point is that an epistemic rationalist, a completely abstract mathematical construct to the best of our knowledge of the physical world, would make a choice that is at odds with an instrumental rationalist, i.e. a real person who's trying to win in real life. Having bounded resources, there is some threshold below which a physically existing rationalist will treat probabilities as equivalent to zero, i.e. will choose not to expend any resources on preparing for such a situation.
A meteorite makes a bad example because it's easy to imagine it happening. Suppose we consider the probability of a three layer chocolate cake spontaneously appearing in the passenger seat of our car during the drive home this afternoon. Yes, the probability must be nonzero, but it's so small as to not be worth considering. All those events with probabilities so small they aren't worth any resources are the ones you never even think about, so they are equivalent to having a probability of zero for the bounded rationalist.
All those events with probabilities so small they aren't worth the resources are the ones you never even think about
... Ah, if only that were so.
(But I take it you mean "the ones you never even think about if you are an optimized bounded rationalist", in which case I think you're right.)
What is the probability that my apartment will be struck by a meteorite tomorrow? Based on the information I have, I might say something like 10-18. Now suppose I wanted to approximate that probability with a different number. Which is a better approximation: 0 or 1/2?
The answer depends on what we mean by "better," and this is a situation where epistemic (truthseeking) and instrumental (useful) rationality will disagree.
As an epistemic rationalist, I would say that 1/2 is a better approximation than 0, because the Kullback-Leibler Divergence is (about) 1 bit for the former, and infinity for the latter. This means that my expected Bayes Score drops by one bit if I use 1/2 instead of 10-18, but it drops to minus infinity if I use 0, and any probability conditional on a meteorite striking my apartment would be undefined; if a meteorite did indeed strike, I would instantly fall to the lowest layer of Bayesian hell. This is too horrible a fate to imagine, so I would have to go with a probability of 1/2.
As an instrumental rationalist, I would say that 0 is a better approximation than 1/2. Even if a meteorite does strike my apartment, I will suffer only a finite amount of harm. If I'm still alive, I won't lose all of my powers as a predictor, even if I assigned a probability of 0; I will simply rationalize some other explanation for the destruction of my apartment. Assigning a probability of 1/2 would force me to actually plan for the meteorite strike, perhaps by moving all of my stuff out of the apartment. This is a totally unreasonable price to pay, so I would have to go with a probability of 0.
I hope this can be a simple and uncontroversial example of the difference between epistemic and instrumental rationality. While the normative theory of probabilities is the same for any rationalist, the sorts of approximations a bounded rationalist would prefer can differ very much.