And that is fully legal.
NO, IT FUCKING ISN'T!
I seriously doubt their soliciting for getting people to fly with them includes notification of that "if you think we're rude then we will not fly you and just take your money".
I mean, think about it. He paid for a service to be transported and they cancelled that contract based on that he tweeted the one person being rude. Why do you think that would be a legal way of doing things? taking money and not delivering their end of the contract? you also think it's legal for them to just sell tickets and then not fly at all?
Now do you think it would be legal for best buy to come to your house and take your tv away because you stated publicly that the salesman was an ass who tried to rudely pressure you into buying extended warranty? fuck no.
and why do you think they back pedaled? because what they did was "normal"? fuck no it wasn't. the criticized person was just using the powers he had for ANOTHER PURPOSE(purpose of keeping the plane safe) to make him delete the tweet that could negatively affect her career.
so next up - when you complain that comcast is a bunch of fuckers online you think it's also legal for them to cancel your internet.... with that kind of attitudes no wonder americans are corporate bitches getting bled dry into debt.