Not true at all.
If you create and/or upload a repository to GitHub, you're giving others the permission to see and fork it. From the "Licensing a repository":
> If you publish your source code in a public repository on GitHub, according to the [Terms of Service](https://docs.github.com/en/site-policy/github-terms/github-t...), other users of GitHub.com have the right to view and fork your repository.
https://docs.github.com/en/repositories/managing-your-reposi...
Also, GitHub’s terms say:
“If you set your pages and repositories to be viewed publicly, you grant each User of GitHub a nonexclusive, worldwide license to use, display, and perform Your Content through the GitHub Service and to reproduce Your Content solely on GitHub as permitted through GitHub's functionality (for example, through forking). You may grant further rights if you adopt a license.”
Part of that reads as if you are only allowed to fork it into other GitHub repos.
Whether copying to your local machine or running are allowed will depend on what “use through the GitHub Service” and “perform through the GitHub Service” mean.
Would also depend on how exactly GitHub (or a court) would interpret "forking", as an argument could be made that a GitHub fork is just a "GitHub Create" + "Git Clone" operation, and having permission to do a "GitHub Fork" means you're also allowed to do a "Git Clone".
I guess we'll never know, as a case like this would never reach court so it's guesses all around.