That's not how it's been on AA of late either; the recent move to no longer officially have saaver awards even had some worried that there would never be availability on AA domestic through BA (and even in the pre-dynamic era, my understanding is that if AA didn't have saaver availability, BA would not show a flight as available while AA would).

The general trend, as airlines move to dynamically priced awards is that own-metal awards (e.g. DL on DL etc.) get last-seat or near-last-seat availability. Meanwhile, because partner awards are basically fixed-price when the program actually buys the ticket, those are subject to inventory controls like they always have been.