Finger trouble at Red Bee seems most obvious opportunity for such a cockup although equally least likely as you wouldn't expect them to have 5 Live on the desk routinely. Unless there was 5 Live content on Red Button last night?
5 Live, and all the main radio stations have been available in pres for years, 5 Live is most often needed as a backup for sports events and radio 2 for Eurovision for example
True, although I thought it was specially routed to the pres desk when required rather then being routinely available on a fader.
There's a suggestion in the link you gave that the same fault was on iPlayer. Unless that means the rewind service, you'd have to suspect an ingest issue? They don't normally use off air recordings for iPlayer for non live material.