Litebulbs pretty much got it spot on, but to clarify, one should review the CAT II/III requirements at the front of the JEPP. An interesting read...
The restriction regarding CAT II/III doesn't completely lie with the aircraft, it lies with the airfield as well. When an airfield is conducting CAT II/III ops, there are certain requirements that have to be met, protecting the ILS beam etc and it's all in the JEPP.
The Airbus is allowed to do a CAT III to a CAT I runway provided the flight crew closely monitors the approach and is prepared to take over. Now, that's just a BIT of an understatement, but it's what's in the Airbus manuals.
You may have a perfectly excellent ILS, but it may not be protected to the level required to do an ACTUAL CAT III. That doesn't mean you can't shoot the CAT III approach in VMC, it just means that someone may pass in front of the localizer antennae in a ground vehicle and break the beam, disrupting your approach. That's why you are supposed to be ready, etc, etc.
Long story short, doing an autoland to a NON-CAT III runway is fine in VMC for certification purposes. Provided it works, that is.
Hope that doesn't muddy the waters....
PB