I would argue that Dr. Dao continued to have a legal right to be on the plane until at least after the purchase price of his ticket had been refunded in cash. At that time, he could possibly be trespassed off the aircraft. But until then, he remained boarded and seated, with a valid lease on that seat, with the default rights of all humans, plus any additional rights granted to airline passengers by US law. He didn't voluntarily leave, because he had no reasonable expectation that he wouldn't actually have a choice in the matter. You can't voluntarily do anything if
not doing that thing is attached to the threat of force.
He refused to be coerced out of his seat, and had to be forced. Voluntarism doesn't enter into it, if there is no meaningful choice.
And then, the instant he's off the plane, they can either hand over another 4x multiple of his fare in cash, and tell the guy to sod off, or they can make a best effort to get the guy to his destination and possibly still pay him something when the alternate transportation arrives, according to how many hours of delay the passenger experienced.
While the media have been quoting $1350 as a maximum, 14CFR250.5(e) mandated reviews in 2012 and every 2 years thereafter, that use the CPI-U index to adjust the maximums. The CPI-U of August 2011 was 226545, and the CPI-U of July 2016 was 240647. So the 1-to-2-hour-delay compensation cap should be $675 * 240647/226545, rounded to the nearest $25, which is $725, and the over-2-hour-delay compensation cap is twice that, or $1450. Inflation.
Furthermore, the airline may offer vouchers and discounts only if their value equals or exceeds the cash value they would otherwise be required to pay, and the passenger is not required to accept them in lieu of cash. I would argue that an $800 travel voucher that expires in one year is worth much less than $800 in cash, especially when the average American travels by air only once per year. I would personally value $800 in expiring vouchers at around $200 cash.