The diff between CAT II and CAT III - is not just signal reliability and monitoring, it is also airport and runway lights, power supply and emergency generators. A very significant part of it is the time to switchover from normal to emergency/standby power. There is a possibility that the airport power supply cannot at a particular time meet the requirements of CAT III - hence a reversion to CAT II. Really who knows....
You would be a brave person to operate to CATIII when CATII is in force.
Legally where do you stand? (Not a leg to stand on I suspect)
Gambling with your passengers lives..........even if it is an educated gamble.