Originally Posted by ajax

That's not how it happened when I flew LHR-AKL via LAX.

We were never allowed out of the (rather large) room. We had our passports checked but there was a special little immigration counter just for our flight, and just to make sure we were who we said we were. The flight came through there at the same time every day We might have technically entered the US but freedom of movement throughout the airport was not allowed.

In any event, the OP was already considering flying via SFO.