I believe BA tag priority bags just for pax in J & F.
I’ve had the exact same comment made as the OP by a check in agent when flying WTP. ‘We can put a priority tag on, but it is the bar code on the actual luggage label that determines the priority of the bag’. By that I suspect it means bags of J & F pax get put in a separate hold container.
Of course, as I suspect we’ve all witnessed over the years, regardless of airline, a bag tagged priority does not always come out first, as ultimately the baggage handlers at the destination airport are responsible for the final delivery of the bags.