If they said P(heads) is 60% and you get 4 tails in a row, you also might think the people running the experiment lied to you, especially if it happens near the beginning. But there’s a 13% chance in any sequence of four tosses.

but that means you should bet into the bias, not against it.

True; my point was that the person falling for the gambler's fallacy was wrong, but in a sense, so were all the people explaining the gambler's fallacy.