Exactly, that's the whole point of git. Your entire code base is distributed (or at least everything you push out to a remote). Unlike CVS/SVN, you have that whole copy and collective history of everything that was pushed in that repo.
If you want to move it, in most cases you can simply create a new bare repo on another remote and push yours to it. It's probably the easiest system out there to simply pick up your data and go, unlike the walled gardens of social networking, video (YouTube isn't video, it's video + annotations + another ecosystem of tools that's not easy to export), and other services.
Even blog software isn't as resilient. You still have to export your Wordpress or Ghost blog when you want to move it. With git, when you work on it, you already have a full copy (with a few exceptions of course, like remote branches people prune without merging or local branches people never push).
To add to the other replies: I'm not trusting them with keeping my code safe (everybody has copies on their own computers). I'm trusting them with facilitating my workflow, helping me collaborate, and also to keep my issues etc. safe.
So yes, this can have a relatively large impact in terms of not being able to work as efficiently for a day and potentially losing some issues, but nowhere near as disastrous as losing all my code.