Well, SAS policies are always a bigger mystery.
Maybe they just want to point to their own top tier customers that they shouldn't fly with other *A airlines. Or then just someone didn't think of that option that someone would be flying with some other airline than SAS from CPH.
Of course the security people are just doing their jobs as instructed, I am sure they would allow anyone through if SAS would have allowed that. Some feedback to SAS would be a good idea?
Similar things exist in other airports too, in HEL SAS is having an EBG benefit for VIP parking
when flying with SAS. It is similar EBG-SK flight benefit as the Fast Track in CPH.