So... Xbox live is down, I am signed in locally and I can't use Plex.

Im sure this is a new feature and at a guess they use the money they get from people testing there new products to finish the new products.

Does your internet work when xbox live goes down may seem a simple question but none has mentioned it.  :D

Yes it does.

That being said, considering they are both on the same network, there shouldn't really be a reason playback functionality on a local network shouldn't be broken when an Internet connection is down. But that is a separate problem.