[cyunem]

It's technically true (the best kind). The more affordable apartments are usually rented out by a 'boligforening' and it's relatively common to give a membership/waiting list spot as a birthday present to newborns when the family lives in or near Copenhagen. This helps getting an affordable apartment when people leave home later to study. But there are plenty of apartments that do not require 18 years of waiting, it's just that the rent is higher.

As for my own experience, I'm moving to Copenhagen in a month for a job and I managed to find an apartment after searching for about a month. I'm moving from Aarhus (the second largest city in Denmark) and my new apartment costs 2.5 times as much each month, for which I'll get a slightly bigger apartment but much further from the center of town. My guess at the reasons for the price increase is ~50% higher rent in Copenhagen, ~30% moving from a 'boligforening' to a non-'boligforening' and ~20% the extra square meters in the new apartment.