Not through the GitHub interface, no. But you can copy all files in a repository and create a new repository. IIRC there's a way to retain the history via this process as well.
That’s beside the point. The article is specifically about « GitHub forks » and their shortcomings. It’s unrelated to pushing to distinct repositories not magically ´linked’ by the GH « fork feature ».
You can create a private repository on GitHub, clone it locally, add the repo being "forked" from as a separate git remote (I usually call this one "upstream" and my "fork", well, "fork"), fetch and pull from upstream, then push to fork.