The confusion about whether an Avios redemption on AA is subject to standard baggage allowance rules (whether BA's or AA's) is something that BA is creating. I routinely use Avios for AA domestic bookings and starting sometime over the last few months, I receive multiple warnings both on BA.com during the booking process, and occasionally from phone staff when I have to call to complete the booking (as is common recently due to IT issues), that these are HBO fares. As pointed out above, they are definitely not HBO fares and I have yet to have any issues checking bags using my standard AA allowance based on OW status.
I can't explain lall's experience other than to observe that it was in PHL, which is a unique place when it comes to "customer service."
Now, it is possible that we're headed to a future system where Avios booking do in fact book into Basic Economy - only BA (and perhaps AA) would know for sure and they're not telling people like us. Or to be more accurate, they are telling people like us that these are HBO fares but the information is incorrect.