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Since AA members can't get access anyway on a domestic itinerary we are talking about OW status members traveling on AA which according to the above formula by Himeno should mean the OW airline granting status and not AA should be paying. But the sticking point was AA not paying.
So it sounds to me that it's always the operating carrier that pays?
I can't say that AA were not paying for non AA *O elites; however they were very likely refusing to pay for their own elites on domestic itineraries.
An email was sent in relation to AAdvantage Elites (or non status PAX in First/Business) on AA domestic itineraries. It simply had the subject "Lounge Access".
Since that nor the content did not indicate specifically who or what it related to, the email was generalised and staff were told to deny all PAX travelling on AA domestic.