But I seem to remember reading on one of the other numerous threads that below a certain airspeed, the stall warning stops. If this is the case, then if they pulled up, with very low airspeed and a nasty AoA, then wouldn't the stall warning stop giving the impression that there was no stall? Then when pushing nose down, the stall warning would start again when airspeed increased above the limits 'causing' them to pull up again to wrongly get out of the stall?
This feature is intended to keep the STALL warning from triggering continuously while rolling on the ground. The speed threshold has been set so low (<60 knots) that it can only be exceeded while on the ground, there is no way you can slow down that much while airborne, not with such a plane. This assumes of course that you have reliable airspeed data, if you have a UAS condition than anything goes and such a failsafe can itself become an issue . As has already been suggested by other posters it would make sense to make STALL warning suppression entirely dependent on WoW status and do away completely with any speed threshold. If your wheels are on the ground then a stall condition becomes meaningless as you're not actually flying, if you're still airborne then a STALL warning should never be suppressed, regardless of the (possibly unreliable) IAS readings.
Regardless of the above I find it hard to believe the hypothesis -- because that's all it is, unfortunately we cannot ask the pilots what was actually going through their mind but can only formulate hypothesis -- that they went back to pulling on the stick because when they pushed the previously suppressed STALL warning became active again. To do so would go against basic training principles that are engrained in any pilot, even a lowly PPL, namely that when stalled pulling will only put you deeper into the stall, only pushing can get you out of it. The only situation where this would not be the case is when flying inverted, but I'm pretty sure the AF pilots were not confused to the point of believing that their plane had turned upside down.