Apparently there's no github web UI to actually copy a repo so it's not listed as a fork, but of course git makes it quite possible, and github even provides directions, using git directly.
I'm imagining a browser plugin that notices when a repo you are about to fork is private, and (or even without that) adds a 'copy' button which gives you text to copy-and-paste into your terminal to make a true copy.
https://help.github.com/articles/duplicating-a-repository/
I'm imagining a browser plugin that notices when a repo you are about to fork is private, and (or even without that) adds a 'copy' button which gives you text to copy-and-paste into your terminal to make a true copy.