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.

That's not the GitHub concept / almost trademark of "fork" anymore though, which is what your parent was talking about

All you should have to do is just clone the repo locally and then create a blank GitHub repository, set it as the/a remote and push to it.

I mean it's git, just git init, git remote add for origin and upstream, origin pointing to your private, git fetch upstream, git push to origin.