Language Driven By Culture, Not Biology

This may be a blow to certain readings of Chomskyan Universal grammar. The article summarising the findings is here: Language Driven By Culture, Not Biology, Study Shows. In sum, this is what the research seems to indicate: "it is unlikely that humans possess a genetic ‘language module’ which has evolved by natural selection. The genetic basis of human language appears to primarily predate the emergence of language."
What I'm not sure about, though, is that although it would appear that biology cannot evolve as fast as culture, does this mean that there is no biological basis for language as such or that there is simply no basis for its diversity? This seems to be what is meant later in the article; "We conclude that slow-changing genes can drive the structure of a fast-changing language, but not the reverse." I think that means that there could be a biologically-based universal grammar of which actual instantiations of language would be declensions. What that would require in evolutionary terms, would surely be merely the evolution of a 'starting point' 'module' for language. Something that would give the basic structures. The fact that there are families of people (admittedly rare) where there appears to be a genetically based language disability in syntax, seems to indicate at least some 'nature' as well as nurture.
But maybe I've misunderstood something here.