Jason Palmer at the BBC reports that a paper in Nature, Evolved structure of language shows lineage-specific trends in word-order universals, casts serious doubt on Chomsy's univeral grammar. It does not. But Palmer's understanding of the paper does highlight the degree to which people do not understand the relationship between the contraints created by our genetic system and the evolution we see at the social level. The presence of spontaneous order, or self-organization, at the social level certainly does not mean there is an absence of genetic contraints as expressed in fixed-plastic neural pathways in the brain.
The article is looking at word-order evolution, and discovers that word-order demonstrates social evolution. The conlusion seem to be that this disproves universal grammar. But this is hardly the case, as word order in and of itself is not an example of deep grammar. Universal grammar involves the universal presence of certain linguistic elements, such as nouns and verbs, subjects and predicates. With these constraints, and considerably flexibility in word-order and vocabulary, which could (and do) evolve at the social level, it is easy to generate the diversity with unity that constitutes human language.
Here is how it works. The genes set constraints on the layout of the neural pathways as the brain develops. Thus, for language, certain elements must appear, such as nouns and verbs, subjects and predicates, etc. These neurons are partially plastic, allowing the brain to adapt to the environment. For a languaging species, langauge itself becomes part of the environment. Elements such as vocabulary and word-order may be more adaptible if more flexible, and so remain in the social sphere. This social sphere is a spontaneous order, meaning that an order emerges, as the patterns of word-order evolution observed in the study shows, yet it is a changing order. This emergent social order interact with each individual's brain to adjust those plastic elements so that individual can learn the specifics of the langauge in that time and place to be able to communicate with others.
In other words, this Nature paper described elements of the spontaneous order of language, but did nothing to overturn universal grammar. We have to remember that we are both genetic and social simultaneously. The presence of diversity in culture does not mean there is no such thing as cultural universals. The presence of diversity in literature does not mean there is no such thing as literary universals. And the presence of diversity in language, let alone a social pattern of evolution of certain elements of language, does not mean there is no such thing as universal grammar.