Booked as codeshare
Yes, it was booked as a codeshare. Specifically, Malev sold the ticket, and thus the ZRJ-JFK leg was listed as MA 4008 and not AA 65. It's AA metal. Malev sold me B and that's what my itinerary (booked through a travel agent) shows. But the boarding passes issued by Malev and then reissued by AA both show H for that leg.
The problem is that I'm originating from CLJ. My travel agent says that there is no way for AA to sell a ticket that includes CLJ -- either Malev sells the entire itinerary CLJ-BUD-ZRH-JFK, or I split it into two tickets.
My goal is to upgrade on the TATL leg. I used to collect all my points in Duna Club, but that was worthless because (1) Malev will only upgrade you on Malev metal on a Malev flight, and (2) Malev won't upgrade individual legs -- you have to upgrade end-to-end. CLJ is served by a propeller plan, and there are never upgrades available. I racked up 250K miles and they are seemingly worthless.
So I switched to AAdvantage thinking I'd be on AA metal and be able to upgrade with AA points on a B class ticket. But Malev passes it through as H, and that seemingly is not upgradeable with 15K miles.