Just thumbing through one of, if not the best book, on aerodynamics written and found this. (Aerodynamics for Naval Aviators)
PILOT INDUCED OSCILLATIONS
The pilot may purposely induce various motions to the aircraft by the action of the controls. In addition, certain undesirable motions may occur due to inadvertent action on the controls. The most important condition exists with the short period longitudinal motion of the airplane where pilot-control system response lag can produce an unstable oscillation. The coupling possible in the pilot—control system-aircraft combination is most certainly capable of producing damaging flight loads and loss of control of the aircraft.
When the normal human response lag and control system lag are coupled with the airplane motion, inadvertent control reactions by the pilot may furnish a negative damping to the oscillatory motion and dynamic instability exists. Since the short period motion is of relatively high frequency, the amplitude of the pitching oscillation can reach dangerous proportions in an unbelievably short time.
When the pilot induced oscillation is encountered, the most effective solution is an immediate release of the controls. Any attempt to forcibly damp the oscillation simply continues the excitation and amplifies the oscillation. Freeing the controls removes the unstable (but inadvertent) excitation and allows the airplane to recover by virtue of its inherent dynamic stability.
The pilot induced oscillation is most likely under certain conditions. Most obvious is the case of the pilot unfamiliar with the "feel" of the airplane and likely to over control or have excessive response lag. High speed flight at low altitude (high q) is most likely to provide low stick-force gradients and periods of oscillation which coincide with the pilot- control system response lag. Also, the high q flight condition provides the aerodynamic capability for failing flight loads during the oscillation.
If a pilot induced oscillation is encountered the pilot must rely on the inherent dynamic stability of the aircraft and immediately release the controls. If the unstable excitation is continued, dangerous oscillation amplitudes will develop in a very short time.
If I'm not mistaken the accident ticks all the boxes, but as I commented before, time will tell. No taking over from the NTSB for me.