In the 1980s, Colin Renfrew re-used the concept of an expansion of Indo-European languages from an eastern homeland to model Neolithic agricultural expansion from Anatolia in the Near East into hunter-gatherer Europe. He carefully hedged his reconstruction with strict caveats in order to avoid earlier methodological and political pitfalls. Renfrew's hypothesis of farming-language dispersal has inspired others heuristically to recruit examples of congruent expansions of language, Neolithic agriculture, and people using other language families and, more recently, to fit the majority of the world's larger language families into this same paradigm. The purpose of this review is to argue against a one-fits-all model by showing how paradigm evaluation has gone awry in the other well-known and academically dominant example, popularly know as the Express Train from Taiwan to Polynesia hypothesis. Further it will be argued, that the reasons for the persistence of the Austronesian language/rice-farming hypothesis result from a cluster of methodological errors. These include an overall failure to heed Renfrew's caveats, over-reliance on a controversial putative linguistic homeland, and failure to deal with parallel evidence impartially resulting in unsupported claims of congruence. False congruence and circularity are particularly likely when the process of dating events in parallel proxy narratives is not independent.