Very odd. Why wouldn’t they want this investigated thoroughly?
Not wanting everything aired in public doesn’t mean they don’t want something investigated, if it needs to be. Don’t automatically equate the two things.
They do want it investigated thoroughly.
Or rather, they are satisfied that the case has already been thoroughly investigated.
They simply don't want all of the (personal / private) material (in part, inadvertently) gathered during the investigation to be made public.
Like how would you like, e.g., video recordings of a coroner using a probe to examine a wound on your dead daughter being uploaded to YouTube?
Regards,