First, the issue somewhat drifted from "to what degree should you update on the basis of what looks stupid" to "how careful you need to be about updating your opinion of your opponents in an argument".

I understand PoC to only apply in the latter case, with a broad definition of what constitutes an argument. A teacher, for example, likely should not apply the PoC to their students' answers, and instead be worried about the illusion of transparency and the double illusion of transparency. (Checking the ancestral comment, it's not obvious to me that you wanted to switch contexts- 7EE1D988 and RobinZ both look like they're discussing conservations or arguments- and you may want to be clearer in the future about context changes.)

I am not primarily talking about arguments, I'm talking about the more general case of observing someone being stupid and updating on this basis towards the "this person is stupid" hypothesis.

Here, I think you just need to make fundamental attribution error corrections (as well as any outgroup bias corrections, if those apply).

Given this, who is doing the trusting or distrusting?

Presumably, whatever module sits on the top of the hierarchy (or sufficiently near the top of the ecological web).

Should she tell herself her hardware is untrustworthy and invite Bob overnight?

From just the context given, no, she should trust her intuition. But we could easily alter the context so that she should tell herself that her hardware is untrustworthy and override her intuition- perhaps she has social anxiety or paranoia she's trying to overcome, and a trusted (probably female) friend doesn't get the same threatening vibe from Bob.

True, which is why I want to compare to reality, not to itself. If you decided that Mallory is a malevolent idiot and still happen to observe him later on, well, does he behave like one?

You don't directly perceive reality, though, and your perceptions are determined in part by your behavior, in ways both trivial and subtle. Perhaps Mallory is able to read your perception of him from your actions, and thus behaves cruelly towards you?

As a more mathematical example, in the iterated prisoner's dilemma with noise, TitForTat performs poorly against itself, whereas a forgiving TitForTat performs much better. PoC is the forgiveness that compensates for the noise.

I don't see why.

This is discussed a few paragraphs ago, but this is a good opportunity to formulate it in a way that is more abstract but perhaps clearer: claims about other people's motives or characteristics are often claims about counterfactuals or hypotheticals. Suppose I believe "If I were to greet to Mallory, he would snub me," and thus in order to avoid the status hit I don't say hi to Mallory. In order to confirm or disconfirm that belief, I need to alter my behavior; if I don't greet Mallory, then I don't get any evidence!

(For the PoC specifically, the hypothetical is generally "if I put extra effort into communicating with Mallory, that effort would be wasted," where the PoC argues that you've probably overestimated the probability that you'll waste effort. This is why RobinZ argues for disengaging with "I don't have the time for this" rather than "I don't think you're worth my time.")

But, as I've been saying in my responses to RobinZ, for me this doesn't fall under the principle of charity, this falls under the principle of "don't be an idiot yourself".

I think that "don't be an idiot" is far too terse a package. It's like boiling down moral instruction to "be good," without any hint that "good" is actually a tremendously complicated concept, and being it a difficult endeavor which is aided by many different strategies. If an earnest youth came to you and asked how to think better, would you tell them just "don't be an idiot" or would you point them to a list of biases and counterbiasing principles?