Compensation Fund or Litigation
In the United States health care is almost exclusively private and tied to your job.
If a person is involved in a serious accident in the U.S and is one of the 49 million americans not covered by private health care then your up for the bill yourself.
Post traumatic mental health is serious, and people who suffer from it need assistance from mental health professionals.
So, who pays?
In Australia, thankfully, we still have Medicare (no thanks to the Liberals trying to kill it off) which includes mental health care cover (paid for by the tax payers of Australia) - that is part of the cost is covered.
Sadly in the United States there is an element of greed in which people think that there is always someone at fault to sue and cash in big time.
In Australia, if not covered by a fund, such a the Motor Accidents Compensation Commission, you can recover for your loss via litigation - however this is not mean you can get rich quick by the old "slip & fall" at your local supermarket. Compensation is just that - putting you back in the position your were in prior the accident (and negligence must shown on the part of the defendant - duty - breach - damage).
American's do sue at the drop of the hat, some to attempt to get rich out of an event they happen to be a part of, and others because they have to in order to get the money to pay for medical care they need.
If I were on that flight, I would be sending a chq for $5,000 to the captain and first officer for saving my life.