Github isn't solely a git server. They also have issues, wikis, etc, that are harder to keep in multiple locations.
Issues are normally mirrored to e-mails (caveat: you don't get mail for your own comments), so you can mostly pick up existing threads if your e-mail address book can find the github users involved. If they didn't obscure recipients (at least within an organisation — because I don't think address-book lock-in is worth inconveniencing paying clients), and made an auto self-bcc of your activity, issues would be entirely disaster resistant.