Humans often defy rational-choice theory by cooperating in simple dilemma games, a paradox that has been explained by theories of kin selection, reciprocal altruism and indirect reciprocity (reputation). Fehr and Gächter claim that human cooperation remains an evolutionary puzzle because people will cooperate with genetically unrelated strangers, often in large groups, with people whom they may not meet again, and without any gain in reputation ('strong reciprocity') - that is, when existing theories do not seem to apply. However, we argue that those theories are rejected for the wrong reasons and that the paradox may therefore be imaginary. This has implications for whether punishment is crucial to promoting cooperation.