Git doesn't have a concept of a preferred repository; your local copy is exactly as valid to git as a git server hosted on github.

The originally intended workflow as I understand it involved generating patches which would be shared via a mailing list.

In practice there will generally be a repository that's considered "canonical" for a project, whether that's the one on the computer of the lead maintainer or some hosted solution.

A basic git server is essentially just a repository owned by a restricted user with SSH access granted to maintainers.. This can allow users to push and pull from a centralised or semi-centralised repository in much the same way as GitHub.