They could easily add a thin layer of foil to the cardboard for RF shielding, without it being a metal case (where the metal is also structural and thus much thicker than you need for shielding).
I'm not so sure about that - according to the pictures in the engadget article someone linked to above, the case is made entirely of stacked cardboard with internal recesses cut out, kind of like a hollowed-out book. The designer of the case says this was to take advantage of the channels produced by corrugation for airflow, so covering up the exposed corrugated edges with foil would likely cause overheating problems.
I guess you could encase all of the internal components in wire mesh, but I don't know how practical that would be.
The system was down for backups from 5am to 10am last Saturday.