I'm also convinced it's PIO..
Go on
https://www.airbus-win.com/ TRAINING-- Training to Basic Flying Skills. It's a video and at 29m15s, You will see a good example of real case of PIO over stick free aircraft after an upset from a vortex.
And at 36m15s, The Airbus test pilot strongly recommends to fly raw rata during line operations. Does BA comply with those recommendations by Airbus?