Wirelessly posted (BlackBerry: BlackBerry8530/5.0.0.1030 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)

"Said differently, had I initially booked on the AA metal that he ended up on, the fees/taxes were $57.10 Instead, the fee was $572.80"

Understood. But for whatever reason you did not book the AA flight for your Dad. You booked the BA flight, and agreed to pay the surcharges associated with that booking. When the BA flight was canceled, BA fulfilled its obligation by re-booking Dad onto IB/AA. Yes, it's a very different product, but AA has already agreed to refund the mileage difference associated with the downgrade. Presumably, your Dad could have opted to wait a day or two in LIS (at his expense) if flying BA F was more important than getting back to PHL on a timely basis.

Because of the AA/BA joint-venture agreement, it's hard to know who actually pockets the YQ you paid. But I would be very surprised if you were to see a refund of that YQ.