Categories not showing when all of the posts are private

I have a blog and all of the posts are private (only logged in users can view them). Still, when the users are logged in, Categories widget is still empty although there are number of posts assigned to different categories.

I tried using the List Categories plugin, but still, categories are not shown in the side bar. Is there another plugin I can use or a workaround for the default one?

Edit: I’m aware of this solution, but it doesn’t satisfy my use case because I don’t want to show the posts, only categories.