I have not been there, but my understanding is that the SAN lounge is jointly operated by both AA and Airspace. It is still listed as an Admirals Club an aa.com:
http://www.aa.com/i18n/travelInforma...s/san-club.jsp
You may find this thread helpful, even if you do not have an American Express Platinum card, because the Airspace representative explains a bit about the shared lounge concept:
http://www.flyertalk.com/forum/ameri...ay-2014-a.html