Let's consider a hypothetical situation - you are inspecting an alien who presents GC with nationality A and a passport with nationality B. Obviously, the place of birth and the date of birth should match, but names may differ. What is the likely scenario from your side? This is what stephg was asking about.

As a side note, when I lost my GC and received a temporary I-551 stamp in my passport at the local USCIS office, I travelled with it several times. The passport was always swiped by the CBP, but the stamp was never looked at and the officer never typed anything in the computer after I explained that I had this temporary stamp. So, I assume that the passport may be linked to the GC in some ways either by the combination of DOB, name, nationality, etc or directly through the passport number (although it could change easily). Could you confirm my assumption, FB?