In Denmark (and I would assume those other countries as well) it varies depending on the factors. If you are a foreigner but are living in Denmark, or if you are staying in Denmark for a job, then you can apply for the rights of free healthcare treatment, but if you are a tourist needing urgent care, and are not a citizen of the EU (or the Nordic countries), or under the age of 18, then you will be billed.

So there definitely is a financial infrastructure to bill in Denmark, even though its own citizens never see it. Without knowing it precisely I would also assume that the bill would be very reasonable compared to a bill for the same treatment in the US.