I don't know exactly how they do, but Casio call that "Anti Shake DSP", so I think this is more than jacking up the ISO and denoising. I know there is "deconvolution" software, but I don't know if it is very efficient, and I think this is too "heavy" for a camera. On the other hand, my suggestion seems difficult to implement too so maybe you're right... All I know is that the result looks pretty convincing, but as soon as I got it back (reparation), I will investigate this further...
Edit: Actually it seems that you are right, according to
this official Casio page:
both models incorporate Anti Shake DSP, which reduces blur by raising the camera's sensitivity and therefore increasing shutter speeds.
So that's good news after all, it means that it is possible to obtain the same result by denoising high ISO pictures :-)
However I get another idea with what is said on this page:
Auto Shutter function automatically records the moment of a smile or the instant when hand shake ceases
Using motion blur detection technology, the camera can automatically take a photo at the instant when hand shake or subject movement ceases. Users can also automatically capture the moment of a smile, the instant when subject movement due to panning ceases, or the moment when their own face fills the frame as they point the camera towards themselves.
Maybe the "motion blur detection" is not easy to do (detecting high frequencies?), but "motion detection" already exists, and with little adaptation (changing how motion is detected, with average luminance in cells) it would be possible to do something similar to that...