If I know Jet Blue, they will take a principled position. If they owe him, they'll make a reasonable settlement in the range of $500 to $5,000. If they don't, this case will be awaiting appeal 5 years from now.
There was no injury. If they interviewed the other passengers, they'll likely say they did not know who this guy was until they read his story in the newspaper. It is hard to be humiliated unless the Plaintiff makes a big deal about it himself, and then who's fault is it?
Like I said $500 case. A $5,000 case if you want to try to get an early settlement to avoid paying your own attorney's bills. Usually things like this get resolved with travel vouchers and letters of apology. The Plaintiff has already humilated Jet Blue, they have nothing to lose by defending this case to the hilt now.
... and all that is assuming the Plaintiff is telling the truth....