A rational prior for "the person asking me directions was just spontaneously replaced by somebody different, also asking me directions" would be very small indeed (that naturally doesn't happen, and psych experiments are rare). A rational prior for "I just had a brain fart" would be much bigger, since that sort of thing happens much more often. So at the end, a good Bayesian would assign a high probability to "I just had a brain fart", and also a high probability to "This is the same person" (though not as high as it would be without the brain fart).

The problem is that the conscious mind never gets the "I just had a brain fart" belief. The error is unconsciously detected and corrected but not reported at all, so the person doesn't even get the "huh, that feels a little off" feeling which is in many cases the screaming alarm bell of unconscious error detection. Rationalists can learn to catch that feeling and examine their beliefs or gather more data, but without it I can't think of a way to beat this effect at all, short of paying close attention to all details at all times.