Danes and on-line casinos

When signing up for on-line casinos, I’ve seen them ban or restrict acces to Danes (the people, not the dogs). Why is that?

I believe because they have a National On-line lottery system (which may offer casino type games).

The company that implemented the system (they are from Iceland) is working with my company right now.

MtM

Why would the on-line casinos care?
It appears from comments at registration pages that the Danes seem to be more able to subvert the various bonus rules or somesuch - one registration had: “And players from Denmark: we’re sorry, but you’re just too smart for us - you cannot open a real-money account”