Just checked a random AFM, in this case of an older A321 and it actually does say
- CAT III with DH:
Minimum Approach Break-off Height: 18ft AGL based on demonstrated height loss from when TOGA is selected in a go-around and windspeeds of 5kt tail, 15kt head or below.
Two autopilots must be engaged in APPR mode and CAT 3 DUAL capability must be displayed on FMA.
In that light a minimum DH of 20ft does make sense. But interestingly enough the FCOM uses 18 ft as DH for CAT IIIb with DH, however our regulatory approval for A319 through A330 is for 20ft, for 737 it is 50ft. Usual operation outside france is of course no DH/75m RVR on all fleets.