Yes I agree, they decline regularly to become involved, but sometimes they do assist (latest Flight Safety has one very small example). I don't think it is necessarily the case that they say "no to such a request is that to participate in a police investigation would compromise the aim of the Act under which they operate which stipulates that ATSB investigations are not undertaken to apportion blame or liability to any person." Rather because they can see no significant safety outcome from an investigation of the incident that would warrant expenditure of the finances.
What specific conditions and protection does ATSB evidence have in a Coroner's Court?
We have to also remember here that Police investigating a death for the Coroner are not always doing so to prosecute someone either, rather to find the place, cause, identity etc.