Depends on how many PoPs they have. Looks like they have 4 easter US.[0] If they are seeing large attacks that Krebs saw a few weeks ago, that could certainly be enough to take down one or two, and then causing redirected traffic to take down the other two.
I used to work for a DNS/DDoS provider, and this was a very real problem. Leave the PoPs that are being affected out, or risk overloading the other PoPs by overloading real traffic.
Before moving the other traffic, you also have to worry about blocking the DDoS traffic otherwise you're just redirecting them to the other PoPs. Mitigating DDoS attacks are not fun, and hard to block.
Some sites intentionally disable that, however, by setting a short TTL on replies. The idea is usually that it allows them to very quickly adjust to hardware failures or load across datacenters but it has the consequence of making your infrastructure comparatively brittle.
If one DNS server is down, use the cached result or another server.
DNS is some of the most distributable, cachable data I can imagine.