I suspect that some of that limitation is operator generated. We have to be cautious here to avoid confusion, as I do not know how your specific serial number airplanes are equipped. The only real answer lies within the Airplane Flight Manual for those serial numbers, and none of us can see that document.
That said, the generic Boeing 777 FCOM that I have, which is current through Revision No. 41, makes no reference to an autoland being required if the weather is below CAT I minimums. The glideslope language is the same, as is the automatic landings with flaps 20 or 30, etc. But there is no reference to CAT I, or, for that matter, to runway width.
The Boeing 777 FCTM, Revision 6, states on page 5.19, under Category II Operations, that "Category II approaches may be conducted using the autopilot or flight director only, with one or two engines".
It is obviously not unusual for the operator to place his own limitations in the company FCOM or FOM or whatever-your-authorities-want-you-to-call-the-manual. It is also common for the manufacturer-specified limits to be interpreted, not just by the pilot but often by the company and its training department, as universal to that type around the world, when they are actually only applicable to that set of serial numbers based on the manufactured configuration. All of this comes boiling to the surface in a matter of days when one is trying to set up a new airline flight ops department, with pilots from different previous carriers and a fleet of airplanes that everyone thought would be just like the ones at their last job...but, secretly, are not.