Given my experience with DNS issues, I am guessing that they are running into dependencies along the way that assume/require DNS be available to function.
I would find it a bit surprising if Facebook didn't have OOB access to their data centers, however.
Next time FB save you passwords in OneDrive and Google Drive as a backup LOL. facebook-oob-password@gmail.com
Laptop + mobile tethering + serial cable to the router + teamvewier for the remote admin to get the access solves problems like this in minutes.
Breaking a gajillion security policies by doing that is a different story though.
It's an IP address management (IPAM) solution that also just happens to be a fantastic, federated (if you want) DNS management system too. Indeed a previous org I worked at bought it strictly to tame the DNS beast - local sys admins could control DNS for their subnets but not affect anything else. If we wanted, we could have had approval processes on top of the change requests - the system supported that too.
I think the security teams finally woke up to the IP address management functionality and were slowly starting to integrate that into the rest of the infrastructure - but I was leaving around then. It was a fantastic system. One of the best hierarchical role-based access control systems in an application I have ever seen; the granularity was amazing yet it was easy to understand/administer. Not an easy trick!