No, your git repository is not a backup. It's a record of the history of your project, but it's not sufficient as a backup.

You could see pushing as making a backup, but even that wouldn't backup the exact state of your repository (private branches, configuration, reflog, rerere, etc..).

If an object gets corrupt, it's almost impossible to fix it, unless you have a copy of that object somewhere.

That's why it's still important to make backups of your repository.

I disagree. Even if you are a couple of commits behind, and you totally screwed, you should be able to recreate it from top of your head. maybe a couple of local git hooks, but still, if you pushed, the most important work should be available somewhere else and you can pull it.

That's assuming you routinely push all your changes and branches -- without exception -- to a server. Of course you can always pull from elsewhere to grab a copy of the repo, but that's no excuse for not backing up your local environment.