There’s a difference between “can’t code” and “can’t work”.
A lot of people use git for version control: super good idea, basically anything else is at best unorthodox, at worst bizarrely stupid.
A lot of people also use github for repository hosting, continuous integration, code review, deployment, packaging, etc, etc. this is more of an opinion thing than a standard practice thing, and there are plenty of other ways to get the same tools, either all in one package or from a variety of different ones, self hosted, in the cloud, or some hybrid in between.
If GitHub goes down, you can make code changes and everything to your hearts content. But you might not be able to run your full integration testing pipeline on it, get a code review, or package your software.
If your local build process pulls packages from GitHub or refreshes a remote repository automatically, it can also powerfully mess that up, but that’s nothing to do with git. You can use “ctrl-c/v” backups and still have a build process that tips over when GitHub goes down.