The visual cues requirements at DH in CAT III are meant for normal operation, I assume.
The thing is that below CAT II minima it is considered that there are not enough visual references to make a safe flare and landing, as you point out.
If there is an autoland warning, the airplane will not land, nor do an automatic roll out, so if it occurs below DH (with the required visual cues, of course, otherwise we would be going around already) it is captain's decision. If he assesses that he can flare, touch down and roll out with the available visual references he can land. This can only happen (in my opinion) if the actual visibility is higher than expected
Probably the most sensible thing to do is to go around expecting a bounce on the runway unless the he can clearly see that a landing is safe.
Besides, in a such an approach after a long haul flight, jet lag, fatigue, etc... our ability to correctly perceive the runway with just a few lights in the fog can be impaired. If the warning is due to a deviation from LOC or G/S during a landing with crosswind, Can we really see how the runway is with respect to the airplane with just three or four lights in sight, correct the flight path and land?