For example, suppose the machine is actually set up to always produce head-biased coins. After observing the coin tosses for a while, a typical intelligent person, just applying common sense, would notice that 90% of the tosses come up heads, and infer that perhaps all the coins are biased towards heads. They would become more certain of this with time, and adjust their answers accordingly. But the frequentist would not (or isn't supposed to) notice this.

They wouldn't (they aren't)?

He or she would answer "the coin is head-biased with probability .9" 90% of the time, and "the coin is tail-biased with probability .9" 10% of the time, and keep doing this, irrevocably and forever.

Only if they committed to this particular rule at the start, I would have thought...? I'm unsure what compels a frequentist to use that particular rule.