Orca, how a regulator or accident investigator appears to be independent of each other or the operator is not the point. They are or they are not. How would it appear if a regulator had for instance allowed its functions to be carried out by say an aircraft manufacturer? If that manufacturer produced an aircraft that lacked airworthiness and then incorporated a badly compromised system in an attempt to ameliorate the symptoms of that lack of airworthiness, I would suggest that regulator lacked independence.
If there followed airworthiness related fatal accidents which were investigated by an air accident investigator that shared a 'rather trivial secretariat role' with the regulator, how objective would those investigations be, given that strong censure of the regulator would then seem to be appropriate?
I apologise for the heavy handed scenario I have painted above. It merely attempts to show that regulator and investigator must be free to point the finger at anyone, including each other. In the case of UK Military Air Safety, given previous interference in that process, such independence is vital. To have been compromised once is a misfortune, to then have it happen again...