Ok, I flew out of T3 again today so had to see for myself. Everything said above made sense but I couldn't picture how it actually works.
There is a small glassed-off hallway which runs lengthwise along the outside wall of the terminal, just in front of where the jetbridge connects, so that arriving pax don't have access to the general departure area (unless the doors are opened). These hallways (one each for E1-E2, E3-E4, and E5-E7 as @
gengar described) connect to the aforementioned elevators. Orange signs point downward to CBP area.
I'd overlooked this hallway before, it's a fairly unobtrusive setup. So, thanks all. Pedantic curiosity satisfied.