Earlier quoted context omitted.
Same in Sweden as well.
I think you are misleaded by the branding on your debit card. Most transactions are not going through Visa, but a third-party solution that the banks them selves run. I might be wrong, but I think Nets delivers the solution in most of northern Europe. They call it NetAxept. This is a direct pay solution used with online terminals, the Visa/MasterCard-part of your debit card is just for offline transactions or credit.
It would be the height of stupidity for Mastercard and Visa to allow banks to issue cards with their labels and then have these cards be part of some secret "strictly Northern Europe" Mastercard/Visa network. Talk about confusing the customers.
But this is all moot: I have both Mastercard and Visa debit cards issued in Sweden. They work perfectly well outside of Europe...