Well, OK, I could understand a position saying "We don't have a special-purpose module of our brain devoted to grammar," which is (I think) a direct opposite of Chomsky's position. I'm not a neuroscientist, so I don't really know how much we're close to answering this.
However, that is very different from the quoted passage. It sounds like these "neuroscientists and psychologists" don't think our brain has any notion of "grammar" at all, and everything can be explained better with statistical relations. I find that very hard to accept, and I wonder if a more reasonable position (= there is no special part of brain reserved for learning grammar) was summarized poorly into a much stronger hypothesis.
Well, of course, if we reduce everything as much as we like, then we could say everything is about statistical relation of a gazillion variables (or quantum mechanics, if you go far enough). But that's not useful, isn't it? Even if we cannot pinpoint a neuron and say "This neuron will fire if it sees a past perfect!", if the brain as a whole acts like it has an underlying notion of grammar, then I think it's fair to say that it "knows" grammar.
And, forgive me if I'm wrong, but I'm pretty sure that my brain acts like it has some notion of English grammar. :P
Edit: Hmm, I think I caused confusion by using the word "innate". Apparently it can mean (1) existing from the time a person or animal is born, and (2) existing as part of the basic nature of something.
Chomsky proposes (1), and many disagrees. (I don't find Chomsky's arguments particularly convincing, either.) But the sentence I quoted (which didn't use the word "innate") sounds like it was against (2).