For a status page to be actually independent, it needs to have all it's requirements hosted on other infrastructure. fb.com authoritative DNS is the same as facebook.com, so it's going down when (FB) DNS goes down (and DNS is going down when BGP is broken, apparently).
It looks like the status page is hosted on CloudFront though, so it got part of the way. (Of course, the other question is if it was updatable / updated during the outage)