BGP takes two to untangle
Gandi.net reported on the issue that they had dropped their BGP routes through CenturyLink/Level3 but CenturyLink was still advertising the dead Level3 routes. This meant that the mitigation built into the Internet for such dead routes wasn't working, so otherwise functional sites couldn't recover using alternate transport. The BGP storm CL unleashed may have caused enough congestion that the good updates simply couldn't get through.
In my case much of the Web traffic was still working, but email from my three main providers had stopped. Yahoo was feeling poorly, a fact that might bring some glee but it was affecting viewing several rocket launch attempts, dammit! At least the morning (USA time) launches were scrubbed, so no lasting damage beyond stress taking a few more sanity and health points.