The company whose plane just crashed, killing three people and injuring over one hundred others, is upset that the mistaken broadcast which was later retracted has harmed their reputation.

To play Devil's Advocate for a bit, why should we let people get away with turning the death of three people into a racist joke?
Sure, in this case it seems like they're going after the wrong people. But if we're talking about the principle of the thing....
They specifically said that they'll never sue the organization that confirmed the names for the news organization.
Yes, the news organization was incredibly stupid for not realizing the joke, and they're internally punishing people for it, apparently. But the initial error began further up the line, and suing the king's fool rather than the king strikes me as being disingenuous and deflecting, trying to drag attention away from any mistakes on the airliner's part.
ASIDE: And by the airliner's logic, even if there was no joke
they should still be suing them for reporting on the issue. The joke didn't make the airliner look bad, it made the news look bad. The crash is what made the airliner look bad.