Wizofoz, all you've said is correct. However the question is WHY take off 125 and CAT III a 200 in other words why RVR 200 is required for CAT IIIa and not RVR 125 like for the take off.
The answer is cause the law maker leaves a back door open for an unlikely event of a manual landing with fail passive shooting a CAT III a. In order to perform such a landing a min of 200 rvr is required (actually its 300 meters established throughout an empirical methods but may be reduced provided an aircraft with a fail-passive automatic landing system which is supplemented by a head-up display which does not qualify as a fail-operational system but which gives guidance which will enable the pilot to complete a landing in the event of a failure of the automatic landing system. In this case it is not necessary to make a go-around mandatory in the event of a failure of the automatic landing system when the RVR is less than 300 metres.) The figure 200 is because of the geometrical position of the pilots eyes which sees the runway's segment in a slant vision. In other words when the aircraft is on the runway the pilots only needs 125 m RVR in order to perform required action consequently when the a/c is at 50 ft with 4 deg pitch the pilot sees a segment of the Rwy in slant vision and therefore 200 RVR m is required in order to take over and land manually. 200>125 because the vision of the pilot at 50 ft is more obscured than on the ground. Perhaps the term slant vision is not appropriate it's obscured one.
Cheers.