Economic experiments have suggested that cooperative humans will altruistically match local levels of cooperation (conditional cooperation) and pay to punish non-cooperators (altruistic punishment). Evolutionary models have suggested that if altruists punish non-altruists this could favour the evolution of costly helping behaviours (cooperation) among strangers. An often-key requirement is that helping behaviours and punishing behaviours form one single conjoined trait (strong reciprocity). Previous economics experiments have provided support for the hypothesis that punishment and cooperation form one conjoined, altruistically motivated, trait. However, such a conjoined trait may be evolutionarily unstable, and previous experiments have confounded a fear of being punished with being surrounded by cooperators, two factors that could favour cooperation. Here, we experimentally decouple the fear of punishment from a cooperative environment and allow cooperation and punishment behaviour to freely separate (420 participants). We show, that if a minority of individuals is made immune to punishment, they (i) learn to stop cooperating on average despite being surrounded by high levels of cooperation, contradicting the idea of conditional cooperation and (ii) often continue to punish, 'hypocritically', showing that cooperation and punishment do not form one, altruistically motivated, linked trait.