This is not correct. All involuntary reroutes are marked as INVOL.

Involuntary in the context of a reroute means that the passenger did not elect to initiate the reroute. So a voluntary denied boarding where you agree to take a later flight for compensation is still an involuntary reroute since the situation that was outside the customer's control (oversale) resulted in the reroute being needed.

A voluntary reroute is one where the customer initiates the desire to change -- e.g., I would like to take the 6pm rather than the 2pm.

Try not to get caught up on that INVOL designation. It is meaningless and does not help your case.