Models of the acquisition of word segmentation are typically evaluated using phonemically transcribed corpora. Accordingly, they implicitly assume that children know how to undo phonetic variation when they learn to extract words from speech. Moreover, whereas models of language acquisition should perform similarly across languages, evaluation is often limited to English samples. Using child-directed corpora of English, French and Japanese, we evaluate the performance of state-of-the-art statistical models given inputs where phonetic variation has not been reduced. To do so, we measure segmentation robustness across different levels of segmental variation, simulating systematic allophonic variation or errors in phoneme recognition. We show that these models do not resist an increase in such variations and do not generalize to typologically different languages. From the perspective of early language acquisition, the results strengthen the hypothesis according to which phonological knowledge is acquired in large part before the construction of a lexicon.