First, having a Danish grandparent doesn't guarantee that you'll inherit an exactly proportional amount of her genes. Your parent (the child of the Danish grandparent) would have inherited 50% of that Danish heritage. But your parent also has 50% not from that Danish parent. It's completely possible that the majority of the 50% that you inherited from your parent could have come from the non-Danish portion of their DNA.

Second, I have a grandparent with Danish heritage. On my test results they also show as Norway. This suggests that Norway and Denmark are likely genetic matches (or at least my family line) if you go back far enough.