Not likely Crab.
You're in one of the remotest parts of New Zealand, where there are no safe places to land, and you wonder why there were no witnesses? Think unpopulated Norwegian Fjords and you have an idea of Milford sound, both in remoteness and topography.
If you go back through helicopter crashes in NZ you will find that in a distressingly high percentage of them the ELT does not go off. Do a google search of Michael Erceg and EC120 to see what I mean.
Missing helicopter may never be found - National - NZ Herald News
They eventually found the helicopter, but the ELT never went off.
Thoughts are that this is due to the placement of the ELT or the severity of the impact. There have been law changes to put them in the fuselage, then put them in the tailboom, then put them back in the fuselage, but none have stopped this ELT failure phenomenon.
And remember, it is a 500. They seem to fall out of the sky quite frequently for no apparent reason
Loss of life and damage to third parties are not the only reasons to carry out an investigation. How about an unexplained engine shutdown in a popular aircraft type that is used to carry thousands of passengers worldwide every year?
CAA do sometimes carry out accident investigations in NZ, but the Transport Accident Investigation Commission is the main office for investigations. They are an independant authority. If they decline to investigate, then the CAA will investigate and release their own report