The professor got the puzzle wrong

The puzzle was not supposed to be about how to tell whether the man was a liar or a truth teller. Hauser's answer is perfectly adequate for that purpose. The puzzle is supposed to be "What one question could you ask to discover the way to your destination?" In that case you need to ask "If I were to ask directions of someone from the other village, which way would they tell me to go?" In both cases they'll point in the wrong direction, so you just go the other way.