My understanding was that AA wanted to keep their lounge, but the airport forced them to cooperate a shared space (or nothing).
Correction here:
For a long time SAN had no problem with AA building their own space, but AA did not want to. What SAN did force upon AA was that the old space needed to be vacated b/c they were renovating the whole area. Knowing AA couldnt get HQ support internally for a new space at the time, AA and SAN eventually chose to work with Airspace b/c they liked the brand/concept and b/c they were willing to co-brand the space. Once SAN understood the Airspace concept, yes, they didnt want to move from the common-use model...but there was a years-long window for AA to build this all for themselves that AA passed on. I found most of this somewhere in the airport board records and by talking to both sides. The record is out there somewhere on the web. AA ppl at the lounge, great as they are, often spin this story a bit for whatever reason.