The correct
PR approach would have been a CEO statement like:
"While our staff did follow correct procedures, clearly we initiated a chain of events that resulted in a passenger in our care getting badly injured. All of United is horrified that it turned out this way. That's not what we're about. While I wasn't there, the buck stops with me. This is my problem to fix."
In a crisis you don't deflect; you step forward and take the punches; they stop pretty quickly once people work out you are morally strong enough to willingly take the hits.