I don't have a magic answer to that one but here are some suggestions:
1) To fly a CAT II or III approach, low vis procedures must be in force at the aerodrome in question. ( I assume this would be the case if ATC is offering it). This has certain requirements regarding shielding of the ground equipment as well as ground movement limitations.
2) Flying an autocoupled approach requires a different set of procedures than a standard manual CAT I approach. Perhaps the crew elected to continue with their current approach rather than change procedures half-way down (if the offer of CAT II was not made early enough)
3) Low Vis approaches normally require crew recency, aircraft recency, and certain system redundancy. Perhaps one or more of these requirements were not met?
Hope this helps,
LH