Sacking the (apparently) insensitive CEO was the path that BP took to rehabilitate its image a while back. Symbolic maybe, fatal almost never, certainly not for the CEO who still gets a handsome payout. But that gesture would only be part of the repair work.
Running a customer-facing organization in today's twitch-oriented 'citizen journalist' culture surely requires a serious investment in managing the social media flow. Airlines are dinosaurs in this respect and, if the market is truly as competitive as they claim, not managing your brand on social media can have tangible impacts.
When dealing with businesses and service providers I understand that sh*t happens. It's how they deal with it when it does that influences my long term loyalty.