I don't think it has much to do with chemical treatment or not. A lot of U.S. cities also have hard water; that depends mostly on the source, with groundwater sources having more minerals than reservoir or lake sources. The main differences in U.S. treatment are that it fluoridates and chlorinates the water, it doesn't normally do demineralization. Also the fluoridation isn't even really a difference in this case: Copenhagen's water supply naturally has high levels of fluoride, similar to the levels that the U.S. adds.

But I agree Copenhagen's water is fine for drinking. I even like the taste. What it's a problem for is fixtures and appliances, which chalk up extremely fast, even compared to other areas I've lived with hard water. Showers, faucets, etc. all needs to be "de-kalked" at least every week, ideally every few days. Even simply leaving a glass of water out on the counter for one day will start to produce chalk lines that take effort to remove. Keeping an espresso machine operational is also a challenge, requiring pretty religious usage of the cleaning cycle with a de-chalking tablet.