Where have you read that as privat you can go below minima ???
or may be you mean that you are not subject to do the Approach Ban... If you are in Moscow Wx minima before or after the OM will not help you for the alternate anyway !
The planning case is a valid one as only 3% of the flight need to be shot on CAT II, but also on long Range after 7 or 8 hours flight if the wx is slighly below minima in Teterboro for example you will have to divert to White plain Atlantic city or back to Boston...quite far from final destination for the pax.. if you are CATII you just have to filled a second alternate Newark and you will land CatII there . much better for everybody !