Over the past several decades, we have argued that cultural evolution can facilitate the evolution of large-scale cooperation because it often leads to more rapid adaptation than genetic evolution, and, when multiple stable equilibria exist, rapid adaptation leads to variation among groups. Recently, Lehmann, Feldman, and colleagues have published several papers questioning this argument. They analyze models showing that cultural evolution can actually reduce the range of conditions under which cooperation can evolve and interpret these models as indicating that we were wrong to conclude that culture facilitated the evolution of human cooperation. In the main, their models assume that rates of cultural adaption are not strong enough compared to migration to maintain persistent variation among groups when payoffs create multiple stable equilibria. We show that Lehmann et al. reach different conclusions because they have made different assumptions. We argue that the assumptions that underlie our models are more consistent with the empirical data on large-scale cultural variation in humans than those of Lehmann et al., and thus, our models provide a more plausible account of the cultural evolution of human cooperation in large groups.