By default any runner can access only to the current repo. Self-hosted runner acting the same. You can give it more permissions if you specify it directly in the code of your workflow. See here for more details.

Or by giving it a specially created token.

The main problem with such runners is that all the computer variables, its entire electronic signature, become available to the public. Of your repository is public.

The picture you provided is about a situation where someone forked your project, made changes to theirs fork, and is trying to contribute to your project. If you have workflows that trigger on a pull request, this option prevents any attacker from spamming your runners.