Lots of smoke a mirrors around all this.
Presumably, the owners have put forward a credible plan for how the arrears of APD will be cleared, within the timeline agreed, and the Government have bought this.
End game, will be a reduction (or maybe some abolition) of APD with no (or minimal) reduction in fares, thus improving margins and yields. That may be where cash flow to clear some of the arrears will come from.
The FlyBe brand is now more toxic, than ever, and the re-branding needs to happen ASAP. That said, if it should all go belly-up again, in 12 months, I can't see Virgin wanting their brand to be dragged through the mud.