While I agree with some of what you are saying, Eduard, I believe that you have opened a discussion thread that will be quite interesting to follow!
 
You wrote: "The idea that the "native speaker knows more grammar than has ever
been printed in any grammar books" is PURE NONSENSE"
 
And here's a response based on recent discussions:  Informed by his/her own grammar, a student can write a sentence such as "Running from the neck to the cheek is a patch of white hair" and the grammar experts can debate about the grammatical structure of this sentence for days!  In this case, the student's grammar informs the structure that the grammarians cannot agree on.  Who knows more grammar? 
 
I think that is what the statement actually means. I don't think it has anything to do with Chomsky's LAD or wiring or anything. 
 
Looking forward to other responses--
Linda
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