In a competence culture, you try to understand your sphere very, very well, including not only the current facts of the matter but how those facts might change under different circumstances. Then you try to understand enough of spheres of people around you that you can bracket what will affect you, and how you will affect them. It's implicitly understood that the functioning of the entire enterprise comes from people doing this.
In anti-competence culture, the functioning of the entire enterprise is mysterious and located somewhere else where it's not your problem. You only know as much about what you're doing as you need to barely keep going. You try to know as little about what's going on with others as possible, and if there is any interaction between you, you try to minimize and even resist it, in the hopes that you will have to change as little as possible or changes will be discovered to be unnecessary or deemed to be too expensive.
You want to stay in the cultures of competence. What the article is describing is just how much of the other kind is out there.