Interesting psychological proposition. I'm not sure I'm able to go along with it entirely (there is no way I'd say Tolstoy wrote Lolita, to make myself sound ignorant) but I will simply own up if I haven't read a particular classic novel.
The same is true with classic films. As a card-carrying film fanatic, there are still one or two celluloid skeletons in my closet, so to speak. Until very recently, I hadn't seen The Life and Death of Colonel Blimp, despite having seen all the other Powell/Pressburger classics, and being a huge fan of them since I discovered their work as a teenager.