That's just one example, construction grammar (not limited to US west coast). The innateness of "universal grammar" can be argued against on evolutionary grounds (how could one universal grammar evolve and end up in the DNA of all humans?), neuroscientifically (how can you encode a fixed grammar when everyone's brain is different and continually changing?), from comparative linguistics (there are many languages and they can be radically different), etc.

If it's not about innateness but about the claims of "internal grammar" from the press release then it because less clear that there would be many people who would reject such a position. I think this is a misleading on the part of the press release. Whether something was innate or learned, I think most people would agree that knowledge of language is internalized. So then the question remains whether you call it grammar or something else, and whether statistics plays a part should have no bearing on that if you ask me.