Originally Posted by christep

Rubbish of course. I did a DONE3 with exactly that routing last year (simplifying slightly: TPE-xHKG-SYD-xHKG-LHR-BWI-JFK-HKG-TPE). Backktracking is only prohibited between TC zones (plus the specific exception of Hawaii). Asia and SWP are both within TC3.
Just insist and ask them to put it to their rate desk. The problem you've got is some front line agent who thinks s/he knows the rules and clearly doesn't. Insist that she consults the internal experts.