Then after the investigation the police complaints should investigate and determine if that is the case.
You are saying that the police should not be trusted to do their job properly.
There is a proper way to investigate and remedy that, and it is not in the middle of a murder investigation. Part of the investigation is to determine how much information is released and to whom is it released. The police should be completely free to do so, in the knowledge that after the matter it can be investigated and remedied if wrong.
Their job is to investigate crime and uphold the Law, if within an investigation a press conference is held to inform the Public of the investigation then ALL legitimate News agencies should be allowed to attend, it is not in the Police's purview to decide who is or is not a legitimate News agency.
Censorship and segregation of a free press is NOT in the Police's purview, neither should it be.

do you?