Generally you are correct of course. However there are some airports that do declare something like "LVP CAT II in operation" on their ATIS. Or CAT III if the weather is even worse. I have seen that at pretty much every german airport. When asked, the ATCOs told me that there is no real difference between CAT II and III, but that they do not want someone to divert because he thinks he is required to use CAT III operation when he is only CAT II approved.
Which, of course, is funny, in light of this discussion...