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It is hard to fathom how 3 pilots could have essentially ridden a stall from FL380 to the ground (sea)

Taking an aircraft of this design and size into a 'full stall' is never done. It is highly unlikely that even the manufactures test pilot could have recovered from that condition. It is not like stalling a 'Cub". Many things happen including most likely the failure of the engines due to disrupted air flow. Swept wing aircraft are notorious for their stall recovery problems.

Maybe because they did not understand what was happening?

Keep in mind why the AP and AT disconnected; that was due to unreliable speed indications. Established procedures requires pitch / thrust config. Also, notice from the report that the plane entered a slight bank (which would entice an amount of sideslip). So counteracting the roll with additional pitch up would seem plausible.

From the report: The recorded parameters show a sharp fall from about 275 kt to 60 kt in the speed displayed on the left primary flight display (PFD), then a few moments later in the speed displayed on the integrated standby instrument system (ISIS).
The pilot was
- handed a plane by the AP/AT BECAUSE the AP could not figure out what was happening to the aircraft.
- handed a plane that had just dropped to Alternate Law BECAUSE the computers could not figure out what was happening.
- handed a plane with unreliable speed indications, thus unreliable stall warnings.
At night, in the dark, in IMC, over water, handed an airplane in degraded state of control, confusing/inaccurate instruments.

Who knows what conclusion he (they) reached, but it apparently was not "we are stalling". It may have been - we need Pitch & power, followed by "we are not stalled, we are diving." I'm not about to second guess the pilots actions based on the little information we have now.

However, one should keep in mind that flight testing of the A330/A340 in a very controlled environment, and clean, they do not exhibit any undesirable characteristics. To those flying light aircraft it is very much like a clean stall on a Piper PA28. With the addition of flap, they do exhibit a dynamic Q break.

Military fighter craft when in full stall with alfa > 45° exhibit a sensation that is markedly different than what is encountered at stall onset in a typical traning situation (e.g., alfa around 15-20°) and leave it pretty immediately.

There is a pretty stable ride, the aircraft is loose in roll but there is less buffeting then when at stall onset, it can be pretty disorientating especially if it is dark. The sinkrate is extreme, one needs to be very consitent and persistent to get out of it.

One thing worthy of speculation: what kind of pitch authority would the A/C have if there was significant tailplane icing? If the pitots are implicated as having experienced some manner of icing, what implications does that have with regards to the tailplane specifically, and more generally with respect to airfoil generated lift?

My understanding that a stalled airfoil continues to generate significant lift; put your hand out the window - palm down - at 45^o while traveling 80 MPH down the highway (what happens?). Problem is that drag beceomes scuh a significant that forward velocity is greatly eroded.