Not. You answer your own question, SafetyCase.
This all comes from a Coroner's Inquest. What makes you think the release of evidence (the CVR recordings in this case) required by a Coroner needs to be authorised for release by those that hold it. Even the military are accountable to one of the oldest legal offices in the world, old chap. Or are you suggesting they should have smothered it?... No, surely not.
Once in the hands of the Coroner it, and all the other evidence 'heard' at the inquest, is in the public domain. Inquests are generally open to the public.
The editorial decision to broadcast any or all of the evidence is another question altogether, but in this case I see relatively little harm in doing so. The plus side of doing so with the CVR recordings was, to best explain to the public what happened, ie: that the pilot was wazzing about when he should not have been. There is a clear public interest here: That was the their expensive hardware that got trashed at a time when helicopters are in short supply in a real war and they, the public, are paying for the clean-up. Also, civil action may follow from civilian family members and that may be fuelled in the first instance by public money in the form of Legal Aid.
Dan