and some also said,My impression is that the only sense in which this sentence is true is if you insist that what goes on inside the black box of statistical NLP is somehow explaining what goes on inside our heads. I see it as essentially parallel to the argument against "neural-style" machine learning. Some neural networks people used to claim (some still do, I hear) that what happens in an artificial neural net is essentially the same as what goes on in our minds. My impression (though this is now outside what I really know for sure) is that most cognitive scientists would strongly disagree with this claim. I get the sense that the majority of people who use NNets in practice use them because they work well, not out of some desire to mimic what goes on in our heads.
statistical natural language processing is not language processing at all, only statistics :P
I feel the same is probably true for most statistical NLP. I don't know of anyone who would claim that when people parse sentences they do chart parsing (I know some people claim something more along the lines of incremental parsing actually does happen and this seems somewhat plausible to me). Or that when people translate sentences they apply IBM Model 4 :).
On the other hand, the alternative to statistical NLP is essentially rule-based NLP. I have an equally hard time believing that we behave simply as rule processing machines when parsing or translating, and that we efficiently store and search through millions of rules in order to do processing. In fact, I think I have a harder time believing this than believing the model 4 story :P.
Taking a step back, it seems that there are several goals one can have with dealing with language on a computer. One can be trying to carry out tasks that have to do with language, which I typically refer to as NLP. Alternatively, one can be trying to model how humans work with language. I would probably call this CogNLP or something like that. One could instead try to use computers and language data to uncover "truths" about language. This is typically considered computational linguistics. I don't think any of these goals is a priori better than the others, but they are very different. My general feeling is that NLPers cannot solve all problems, CogNLPers don't really know what goes on in our minds and CLers are a long way from understanding how language functions. Given this, I think it's usually best to confine a particular piece of work to one of the fields, since trying to solve two or three at a time is likely going to basically be impossible.