The private owners of the line in question are the government of Denmark and the smaller towns around the city of Copenhagen.

Yeah, I hate it as well how the Finnish railways is organized. By it being a "Ltd." type of organization, it manages to incorporate the worst sides of both private ownership and public ownership in one. Almost any solution would be better than ours.

But it's still not private. Words have meanings and if we misuse them, we lose our ability to protect ourselves for example from actual privatization.