You should have spoken to AA, who would have told you that discount/airport upgrades offered by AA do not earn as per the higher class but only the underlying paid for fare class.
I wouldn't expect the majority of BA customer service reps to know all the details for all other OneWorld airlines and partners.
The AA earning table is correct. Your boarding pass may have shown you as being in J, but your booking code remained Y (or more likely a lower discount economy fare code).
I talked to AA, who told me it depends on BA as they run the executive club. I was booked into class C.
My problem is not that service reps do not know everything but rather that they - on two different occasion - are actively providing wrong information when being asked. There are surely a big number of cases like this and I still find it quite scandalous that the service reps do give false information when being asked exactly that question.
Again I just lost the possibility to upgrade another flight - and move up a tier - as customer service rep told me it would not be necessary as I would collect points on the AA flight. Customer service is not only not doing their job but doing it wrongly and misinforming people.