Agree completely; generally diminished responsibility is a matter for the defence to prove in a case of murder; it certainly is here in NSW. Not sure if that is the case in all states.At the risk of tearing the proverbial out of this discussion, there is a difference between (A) manslaughter/culpable homicide where a death has been caused unintentionally by gross negligence: in English legal parlance "gross negligence manslaughter" -
and (B) manslaughter/culpable homicide with the intention to kill where a partial defence applies, such as loss of control or diminished responsibility (as in the eventual outcome of the Blackman case), but short of actual insanity which would be a complete defence in law: "voluntary act manslaughter".
Mens rea, which you rightly mentioned, is therefore an element both of murder and (to a lesser extent) of voluntary act manslaughter. By referring to "credible information of murder by..." and "a realistic prospect of a criminal investigation obtaining sufficient evidence to charge [redacted] with the war crime of murder", Brereton is clearly satisfied that the alleged acts appear to have been voluntary* and therefore would amount to murder if proven in court and absent any successful partial defence of diminished responsibility.
If Brereton's inquiry had been informed of any manifest signs of diminished responsibility involved in the offence, that could have been taken into account, but it was not for that inquiry to second-guess any conceivable future defence, nor did it have the power to require persons of interest to undergo psychiatric examination.
Finally, having looked at the Inquiry's terms of reference I don't consider that it exceeded its remit. Concerns expressed in this thread about the report's public contents would apply to the redaction regime, not to its actual contents.
* PS - "Critically, the report apparently finds none of these killings occurred in heat of battle, none occurred “in circumstances in which the intent of the perpetrator was unclear, confused or mistaken”, and all persons involved understood the relevant law of armed conflict and the rules of engagement." Australian war crimes in Afghanistan: The Brereton Report
Each state has its own criminal laws. The NSW law is simple and very similar to the English law on which it is obviously based. Generally, there are three distinct intents that define murder; there are four separate intents that qualify as murder; the intent to commit GBH, the intent to kill, the reckless endangerment and the intent to commit a serious offence (usually one with >25 tariff) that leads to a death. Queensland has added more; I think there are 7.
WA defines three homicide offences: Wilful Murder, Murder and Manslaughter. Wilful Murder covers only for intent to kill. Diminished responsibility would apply as a defence to Wilful murder, reducing the offence to Murder. It might also reduce an offence of Murder to Manslaughter.