Well, that's "involuntary compensation" regulated by DOT. And those are usually handled before you board on the plane. So technically if you walk down the plane yourself, they can call it "voluntarily".

What? What do you mean by "walk down the plane"?

It's involuntary if they don't let you on the place, but if you willingly walk off the plane it's voluntary.

If what the person is saying is true, then technically speaking, the only one who could demand cash would be the doctor.

I disagree. United chose the other passengers who were to be removed as well, and so none of the chosen passengers volunteered to leave the flight as there was no alternative (default) option presented in which the passengers would remain on the flight. Threatening to call the authorities if someone doesn't leave doesn't qualify as eliciting a voluntary exit.

I'm not arguing for or against, I was explaining what the other poster meant since it seemed as if their meaning wasn't clear.

My statement about the doctor being the only one that could be compensated was definitely tongue in cheek.

Only if you were involuntarily denied boarding. The $800 offer is just that, an offer, and the carrier can set their own terms.

Isn't that what happened?

No, denied boarding means they won't let you board in the first place. In this case, he already sit in his seat.

While I suspect you're correct in this instance, that's not actually the point I was making. A lot of people have been going around the past few days saying, "I accepted a $20 voucher for my cancelled flight; was that illegal and they should have paid cash?!?!" People seem to have no notion of voluntary exchange.