Well, hence my reason for arguing that it's a stopover in LAX instead. My girlfriend and I were originally ticketed on a domestic stopover on the outbound and that seemed to be legal, no problem (no backtracking on that one). However, we had a change of plans, hence the desire to do the (potentially) backtracking itinerary.

Goodness knows what the actual rules are, since the UA site does not address domestic connections/stopovers vs international.