The list covers more than just the commercial operators. It includes all aircraft 'operators who performed an activity that is covered by the EU Emissions Trading Scheme, including private entities (and, as DaveReidUK says, some entities that are not aircraft operators at all, because the EU-ETS provides for the owner to be treated as the operator if the actual operator cannot be identified).
The list has always contained plenty of inaccuracies. Probably not that helpful for your quest.
I agree a central source of all AOC holders would be a useful thing. I doubt if such a thing exists, at least not in the public domain. Actually, I have never come across such a listing, even in 'official' circles.