Sounds fishy to me...at least the reason you mentioned.
If aircraft is CATIII capable and approved and we have a CATII chart on board for HHN, what else do you need?
Chart on board usually means that the runway has been approved for corresponding AWO from Etihad's POV. Crew are definitely qualified and A/C should be at least CATII approved (not 100% sure though).
How about we're only CATII approved in HHN and that day it was CATIII conditions...? In that case diversion would be inevitable...Just an educated guess...