The facts of the situation were this:
1. United offered vouchers up to $800 - this is the volunteer phase.
2. They received no volunteers.
3. Moving on from the volunteer phase, they selected 4 passengers to be removed from the flight.
4. They informed those passengers they needed to get off the flight (so now they're covered by the DoT minimum compensation, which is unrelated to #1).
5. Mr. Dao refused to VOLUNTARILY leave his seat, but 3 other passengers did.
6. Police were called, video was taken, lawsuits were started.
"Voluntarily" in the sentence you're quoting doesn't refer to #1 above, it refers to the fact that Mr. Dao, after being told by a gate agent to leave the plane, did not do so. It does not have any relationship to the DoT "volunteer" rules, it has to do with whether he was willing to leave the plane after being told to do so by a person who was empowered by their employer to get people to leave the plane (although their exact legal right to do so remains somewhat grey).
edit: your -> you're