I'm afraid the server was literally unreachable, so cookies are irrelevant. DNS could have done it, but that should have only changed when they migrated. But that was pretty long ago and DNS caches rarely last beyond 48h. Besides - I've seen the website on the new servers before the outage, so the correct DNS entries have definitely made it to me.
Btw - I'm a web developer myself, so if this is an unsolved mystery, I can provide more detailed info the next time it happens (my DNS, Fiddler output, etc).