This paper examines a puzzle pertaining to the distribution of covalued nominal expressions in two understudied Mayan languages, Chuj and Ch’ol. While Ch’ol behaves entirely as expected with regards to the binding conditions, Chuj appears to consistently tolerate violations of Condition C, often privileging linear precedence as the determining factor in the distribution of R-expressions and pronouns. The Chuj data therefore initially seem to cast doubt on a long tradition to treat the binding conditions as universal (e.g., Grodzinsky and Reinhart 1993, Reuland 2010, 2011). I argue that the difference between Chuj and Ch’ol can be largely explained if, contrary to Ch’ol, Chuj exhibits ‘high-absolutive’ syntax, independently proposed to account for a number of morphosyntactic phenomena in a subset of Mayan languages (Coon et al. 2014; Coon et al. 2021). High-absolutive syntax creates configurations in which the internal argument asymmetrically c-commands the external argument, bleeding otherwise expected binding relations from the external argument into the internal argument. The violations of Condition C in Chuj are thus only apparent. I further argue (i) that linear precedence effects in Chuj are a reflex of a more general anti-cataphora constraint on free nominals, which can also be shown to apply to Ch’ol, and (ii) that there are corners of Chuj where the binding conditions do apply, and that in such cases linear precedence is irrelevant for the distribution of covalued nominals. This means that the binding conditions are active in Chuj, even though idiosyncratic syntactic properties of the language often render their application impossible. The general lesson is that despite initial evidence to doubt the universality of the binding conditions, a universalist approach not only can be maintained, but is supported by the Chuj data.