Roy Hudd has got it about right - BA are 100% dependent on US routes where transatlantic passengers pay serious money for 'premium service' travel. If you bite the hand that feeds you, the day will come when the zoo visitors find more friendly animals to throw titbits at.
Anti-American sentiment is increasingly fashionable in the UK among trendy-lefty dorks who actually believe all they hear on the BBC. Unfashionable as it may be, I personally believe America to be the greatest ally the UK has ever had. Knowing American sensitivities over this type of thing I am frankly embarrassed. To actually joke in the cockpit about bombing the White House, and worse still to do so whilst in US airspace, is crass buffoonery of the worst order.
Incidentally, people do care what was said in jest - it matters in a big way to Americans and they are the people keeping BA afloat. Foolish words over such a sensitive issue could be disastrous for BA - and their employees will only have themselves to blame if it is.