First thing Oscar needs to do is have a senior experienced manager do a quick but thorough internal investigation of what really happened at the gate and on the airplane. Someone who isn't in the operations chain of command. Someone who is allowed to speak truth to power.
Separate from that, he needs to have a senior experienced manager (not in the PR shop) do a quick but thorough internal investigation of why, in less than 30 days, United's public relations enterprise responded poorly not once, but twice in response to adverse public reaction to an event involving United. As part of this exercise he needs to figure out why he's getting such horribly tone deaf press statements to sign off on.
At the same time, he needs to charter a team to look at the policies that are blowing up in United's face, and do something about them. This will be difficult, because it is probably going to result in taking decisions that cost $$ and give line employees more autonomy to solve problems as they are happening.
Do that, and it will produce a better environment all around.