I don't know why UAL didn't raise the compensation offer, but they didn't and all the passengers were warned what could happen. They all chose to take their chances and one guy lost.
And here was where they made the mistake. From reporting, they offered $800 and it wasn't enough, so they stopped offering.
$800 was the line where they thought that forcing people from the flight was a better choice than offering more compensation.
Just how much is that choice going to cost them? I'm willing to bet it's going to be millions.
Now, not every time is that choice going to be THAT costly, but forcing people off the flight unwillingly is ALWAYS going to cost them more than the extra incentive.
For want of a nail the shoe was lost.
For want of a shoe the horse was lost.
For want of a horse the rider was lost.
For want of a rider the message was lost.
For want of a message the battle was lost.
For want of a battle the kingdom was lost.
And all for the want of a horseshoe nail.
This was monumentally a bad choice.
Incidentally, I'm on the side of the airline can kick anyone off for whatever reason (legally) that they want. But it had better be a REALLY good reason if you're going to do so because the consequences are dire.
(Note, I'm not certain that, legally, the doctor here has any recourse
against the airline. But not paying out to him doesn't mean they don't pay. I'm pretty sure United is already paying for this choice. On the plus side, they're probably not going to have to worry about overbooked flights for a while.)