Well the serving officers do train as accident investigators and complete the very same course as their AAIB colleagues. They also share the same building, facilities, tea bar and occasionally the milk. The AAIB routinely support their military colleagues and the reciprocal is also true.
I think you are mistaking them with the board members who are deliberately taken from areas of relevant expertise and, typically, the board president is drawn from a different service too. They are also the fresh set of eyes but they do not try their hand at kicking over metal at an accident site and having their best guess - that is left to the professionally trained and experienced individuals drawn from the military and civilian side of the AAIB.
Please note that the Clutha accident suffered significant third-partly casualties and took place in a built-up area, so the legal public interest test is different.