Universal grammar in the way that Chomsky suggested, a sort of structure all humans must have in there brain, is not a thing. But I believe there is something like the "universality of grammar" where the human vision system or motor system can have a grammatical quality to them. In that sense that there is ambiguity in which tree structure represent the world. I've seen this in many places but I am not sure if someone has put this into (better) writing.