Dutch roll is a different oscillation than PIO is. Dutch roll is one of the natural oscillation modes of an aircraft in flight. PIO is an oscillation that results from a pilot's attempts to control an aircraft.
To help understand the difference, take a look at this Wiki post
Dutch roll - Wikipedia, the free encyclopedia, Then compare with the Aristotel definition. This is the reason Aristotel does not describe Dutch roll as a PIO characteristic, and why the Aristotel database does not have accidents listed that result solely from Dutch roll.
I've seen no evidence in the record that AF447 suffered from Dutch Roll. The A330 aircraft has an independent BYDU unit to provide yaw damping. Normally yaw damping alone is sufficient to prevent Dutch roll, although one jet I flew had "stability augmentation" on all 3 axes (and flew the same way a drunk walks when it was switched off.)