Nabokov's words are in his letter to Katherine White (of the New Yorker) on 17 March 1951. He is disappointed (to put it mildly) that she hasn't appreciated "The Vane Sisters".

 

He says he does not understand what she means by (his) "overwhelming style". He writes a sentence which it occurs to me might have been, and still might be, made more of by people discussing Nabokov: "For me, 'style' is matter." (Beckett's remark on Joyce's Work in Progress is endlessly quoted: "Form is content, content is form." I expect Nabokov was alluding to this.)

 

Nabokov explains his purpose in "The Vane Sisters", culminating in the acrostic of the last two paragraphs.

 

He writes: "Most of the stories I am contemplating (and some I have written in the past -- you actually published one with such an 'inside' -- the one about the old Jewish couple and their sick boy) will be composed on these lines, according to this system wherein a second (main) story is woven into, or placed behind, the superficial semitransparent one. I am really very disappointed that you, such a subtle and loving reader, should not have seen the inner scheme of my story."   

 

He points out that one New Yorker reader of his story "finds it unusual that a college girl wears a hat at an exam". Nabokov retorts with a bit of the social reality so well known to him, as a seasoned lecturer to, and examiner of, college girls: "They all do it when they want to catch a bus or a train immediately afterwards."

 

He writes: "I am really quite depressed by the whole business.... what matters most is the fact that people whom I so much like and admire have completely failed me as readers in the present case."

 

So Nabokov is not here "announc[ing] that there's always an important story lurking behind a manifest plot", as Jansy puts it, but he is saying that in some of his past and most of his future stories there was or will be such a "second (main) story". 

 

It's worth comparing this with Freud's notion, in the "Elisabeth von R." case in Studies on Hysteria (1895), of the real "Leidensgeschichte" (passion narrative, existential history of suffering) discovered by his "archaeological method" as a deeper layer beneath the "banal Leidensgeschichte" that the "patient" and everyone else already knows. Only by his encouraging her to tell the "deep", "buried" "Leidensgeschichte" can the "patient" be "cured". It is what "Anna O." called the "talking cure".