Lidz et al. [Lidz, J., Waxman, S., & Freedman, J. (2003). What infants know about syntax but couldn't have learned: Experimental evidence for syntactic structure at 18 months. Cognition, 89, B65-B73.] claim experimental substantiation of an argument from the poverty of the stimulus, in the sense of Pullum and Scholz [Linguist. Rev. 19 (2002) 9]. They cite a specific feature of English-the assignment of appropriate antecedents for anaphoric one-that cannot possibly be learned from experience because the evidence needed is found only in utterances of a type too rare to be encountered. Their argument involves three empirical claims. In this note we dispute all three.