CAT III definitely guaranties rollout guidance.
no, THAT'S Bollocks.
I have operated to CatIIIa with no rollout guidence (B737-300/700 specifically-the CatIIa options don't even have a rudder channel)
That's why you require the 200m vis- to establish lateral guidence.
Though in theory a it can have no DHnever seen a CatIIIa operation with a DH less than 50', To do so you must have an aircraft certified as Fail- operational- in other words any aircraft capable of CatIIIa No DH is basically capable of CatIIb.
From the Royal Aeronautical society:-
For Cat 3a operations involving the use of fail-passive automatic landing equipment, the minimum RVR which is
normally acceptable for operations with small or medium size aircraft is 300 metres. If the aircraft system
demonstrates an in-service record of high reliability, such that the probability of a system failure during the early part
of the landing flare can be shown to be very low, consideration may be given to a reduction in the RVR.
For Cat 3a operations using fail-operational automatic landing equipment which does not include automatic roll-out
control or guidance, the minimum RVR is 200 metres.
For Cat 3a operations using fail-operational automatic landing equipment, with fail-passive roll-out control or
guidance, the minimum RVR is 150 metres.
My bolding.