Interjecting with my area of expertise, modern broadcast media have dictated that reality is inconsequential and perception is everything.
BA is currently perceived as the ultimate in safe air travel, perhaps even more so outside of its home market.
This could change, and could change very rapidly. You may consider this not to be based on reality (SOPs, 3-engine ops, ETOPs arguments etc.) but, as I've stated, this won't matter in the final outcome.
Personally, and this is based on reality, I would step onto a BA operated aeroplane without hesitation, and before any other airline in the world.
But the public who keep the airline afloat may begin to think differently.
It would be worth for a bean-counter to commoditise the value of negative reporting vs. the value of a return to LAX (e.g. in this case). They might be surprised at the answer....