Same is true for subversion. In both cases you can develop and test your code and review your changes against what was last seen original copy.
It's admittedly been a while since I last used SVN, but it was not at all like Git; it was entirely centralized and required server access to do almost anything. Not every developer has a full copy of the repo, as they do with Git. It was pretty slow when I used it too (though nothing like ClearCase).
With Git, you can check in changes, create branches, etc. all you want without needing any network access at all. You only need network access and server access when you want to share those changes with others. This just isn't possible in a centralized version control system.
Github changes git into centralized subversion-like system
No, it doesn't. It facilitates sharing between developers, and that's all. This is not like a centralized VCS, where you need server access to actually do version-control.
but if it is down, your cooperation workflow is going to suffer badly.
No, not really. The whole point to the GitHub (or similar) server is to provide a single point to facilitate sharing. Without it, you'll need to do pushes and pulls directly between developers' machines, which obviously is inefficient, but is doable. However, it's also trivial to switch to a new central server at any time: just stop using the old one, clone the latest version of the repo (which whoever last pushed to GitHub would have) to the new server, have everyone point to the new server, and you're done. That's something you can't easily do with a centralized VCS.