This result upturned the first preference vote which by a majority of first preference votes placed C above B.

The first preference votes do place C above B, but not by a majority; only 8 out of 20 people gave their first preference to C, but a majority means more than half - at least 11 out of 20, in this case.

If C did have a majority of first-preference votes then all reasonable election systems would declare him the winner, including the three discussed here.

It's also worth noting that in real life, people know which system is being used and can vote accordingly; there may be incentives to fill out your ballot paper in a way which doesn't represent your true preferences.