I called AA today. The AAgent seemed to be new.

Eventually she quoted some internal document dated July 9th stating specifically that LGW/LHR would be counted as one of the segments of the 20.

She said this was British Airlines 'fault' and that other partners (i.e. Qantas) might have different rules.

Again, she seemed like a new AAgent, but it was clear that she was reading something in ref to July 9th.

So from AA's perspective LGW/LHR are a segment.

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OT
The AAgent also stated that all printed tickets (i.e. more than 16 segments) were on hold until Oct 16 (hand writer was on vacation). If I bought it now I would have to go to the airport to get them printed.