By definition, if you volunteer you have not been denied boarding. You chose to accept rebooking and you do so on whatever terms you negotiate. Hope the numpties didn't spend "their" EUR 600!

If you are denied boarding, you are entitled to both a duty of care which would include hotel and meals appropriate to the time of day, and cash (equivalent) compensation.

Whether the EC 261/2004 compensation is paid at the gate or by bank transfer later is immaterial.