Petrographic analysis of Formative Mexican ceramics by J. B. Stoltman et al. (see the companion piece in this issue of PNAS) refutes a recent model of Olmec "one-way" trade. In this paper, we address the model's more fundamental problems of sampling bias, anthropological implausibility, and logical non sequiturs. No bridging argument exists to link motifs on pottery to the social, political, and religious institutions of the Olmec. In addition, the model of unreciprocated exchange is implausible, given everything that the anthropological and ethnohistoric records tell us about non-Western societies of that general sociopolitical level.