Of course not. The task would be enormous and, unless the person had eidetic memory, virtually impossible.
However, allowing for a little hyperbole, I think it's possible for a person to claim that and to quote many meaningful passages. They may believe that they've memorised the whole thing. Even I, who haven't read the Bible in almost 60 years, can still recall many passages that I took the trouble to memorise in my 20s, so that's no big deal.
These days I find that -- like poetry that has perfect metre and rhyme -- Bible quotes are more useful for comedy than "wisdom".
But the phone book? What would be the motive?