The decentralized design does avoid single points of failures, and everyone does have a copy. So - check, check, great. Unfortunately (maybe..) everyone has put their master repos in the same place, which somewhat counteracts the decentralization. But there is certainly no immediate coupling between the Git repository on your computer and the Github repository it's pulling from. It's not like Github being down in any way prevents you from working on code you've already checked out, unless you need to go check out more code.
(The same obviously may not be true for package managers and build scripts that are not running in isolation from your upstream repository, which is where the problems have arisen.)