Gentlemen, I do not apologize for AA nor do I set the rules. I am merely trying to explain them so other travelers are not surprised and end up feeling cheated.
I am fairly familiar with this policy flying regularly between LHR and Hawaii and get caught whenever I have an overnight in LAX (Straight through is a tough one after a hard week). I refer you to AA website URL
The salient paragraph for BAEC members being “Credentials required: oneworld customers must be departing on a oneworld operated and marketed flight and, produce government-issued photo identification and, an Emerald or Sapphire frequent flyer membership card or, a First or Business Class boarding pass for the journey’s international segment on the same day or before 6:00 a.m. the following day. Stopovers are not permitted. ”
There is also an exception for LAX-JFK passengers but I cannot quote chapter and verse on the One World rules there.
To MartinSinclair’s question, the US Air Travel Market makes huge differentiation between Domestic and International services in terms of product offering, margins and services. In the same way that BA and European carriers offer more luxurious eite cabins on flights outside of Europe. For example a BA flight of 3 hours 55 to Cairo warrants a 777 with Club World and First yet a 4 hour flight to Moscow warrants a 767 with Club Europe.