The wording is a bit unclear (rushed, no doubt) but I expect this means the DNS servers stopped announcing themselves as possible targets for the anycasted IPs Facebook uses for its authoritative DNS [1], since they learned that the network was deemed unhealthy. If they all do that nobody will answer traffic sent to the authoritative DNS IPs and nothing works.
[1] See "our authoritative name servers that occupy well known IP addresses themselves" mentioned earlier
The anycasted IPs for DNS servers make sense to me and the BGP withdrawal too when the common cases are perhaps one or a few PoPs lost connectivity to the backbone/DC rarely every one of them fails at the time.
I was hoping perhaps the DNS servers at PoPs can be improved by responding with public IPs for other PoPs/DCs and only when that is not available start the BGP withdrawal. Or I can presume the available DNSs at PoPs decrease over time and the remaining ones getting more and more requests until finally every one of them is cut off from the internet.
[1] See "our authoritative name servers that occupy well known IP addresses themselves" mentioned earlier