I tried to verify the claim. At least for Sweden, their universities still have an acceptance rate, with the highest being 80%, and the next highest being 35%[0]. Denmark's highest acceptance rates are in the upper 70s, low 80s[1].

Yes the acceptance rates are relatively high, but the fact that they have an acceptance rates for their universities suggests that not everyone who wants to go to university can.

0. https://www.sabonews.org/universities-in-sweden-with-high-ac... 1. https://uscollegeinternational.com/universities-in-denmark-w...