The narrator in "Paul's Case" might know everything—like the fact that the teachers are "in despair" about him (1.8), but it sure doesn't tell everything. In fact, this narrator leaves out big chunks of information, especially about Paul's after-hours activities and his fears.
One of the most eyebrow-raising omissions is the account of Paul's nights in New York. We know for sure that he's not just staring out the window, because we learn that he falls in with a "wild San Francisco boy" who's a freshman at Yale. But what do they do? We have no clue. All we know is
[T]he two boys went out together after dinner, not returning to the hotel until seven o'clock the next morning. They had started out in the confiding warmth of a champagne friendship, but their parting in the elevator was singularly cool. (1)
If this sounds like a bad case of the morning-afters, it's not just you. Plenty of scholars have suggested that something illicitly sexual is going on here, like maybe the wild Yalie and Paul got a little too friendly—or maybe Paul wanted to get a little too friendly, and the other boy turned him down.
The point is, we don't know. And this lack of information gives the narrator a kind of clinical voice, like a doctor or psychiatrist (or detective) who's presenting the facts of a case to an expert audience. So maybe the narrator doesn't actually know what happened here. He (or she) has to guess and conjecture—just like we do.