The 2005 articles by Stoltman et al. and Flannery et al. to which Neff et al. (this issue) have responded are not an indictment of instrumental neutron activation analysis (INAA) but, rather, of the way Blomster et al. (2005) misuse it and of the hyperbolic culture-historical claims they have made from their INAA results. It has long been acknowledged that INAA leads not to sources but to chemical composition groups. Based on composition groups derived from an extremely unsystematic collection of sherds from only seven localities, Blomster et al. claim that the Olmec received no carved gray or kaolin white pottery from other regions; they also claim that neighboring valleys in the Mexican highlands did not exchange such pottery with each other. Not only can one not leap directly from the elements in potsherds to such sweeping culture-historical conclusions, it is also the case that other lines of evidence (including petrographic analysis) have for 40+ years produced empirical evidence to the contrary. In the end, it was their commitment to an unfalsifiable model of Olmec superiority that led Blomster et al. to bypass the logic of archaeological inference.