To be fair,
git is not the only guy out there...any version control system will do.
Even svn can do this except you lose the lovely aspects of distributed version control software like hg and git offer.
When version system wasn't invented? You just have a shared file system and you coordinate with people. diff is an old software from the 70s.
You can still keep committing locally.
Provided that you have a copy in the first place and you have the most-up-to-update version. Otherwise, you need to get it from someone else.
You can add another remote (e.g. BitBucket, a shared directory, or just a USB stick) and keep collaborating.
You can run local server to handle incoming and outgoing.
You can even share patches by email if you want.
Patch exists before git, just use diff.
Don't get me wrong. I love git. It's nice. I also like github. I just think we ultimately have to remember sync is an issue regardless which VCS we use.