Rand et al. (2013) present a finite population model to explain the evolution of fair behaviour in the ultimatum game. They find that mutation and selection can balance at population states that resemble human behaviour, in that responders on average evolve sizable thresholds for rejection, and proposers make proposals that on average more than meet the threshold. Their mutation however is global, and therefore biased. We show that when mutations are local, thresholds as well as proposals are considerably lower. In order to still arrive at averages in the simulations that match the averages we observe in the lab, we would have to resort to intensities of selection that are so low, that a match between the averages over time in the simulations and the averages found in experiments stops being an indication that the data are in line with what the model predicts.