Andt RR,
Unfortunately, Australians have no constitutional protection similar to the Fifth Amendment to the US Constitution.
The Australian common law rights against self incrimination are very limited, and statute law trumps the common law, unless it is found to be unconstitutional by the High Court of Australia.
Indeed, there is a large body of law here, both State and Commonwealth, where you can be compelled to answer, including being forced to incriminate yourself, with attached severe penalties for non-compliance.
Sadly, the whole US ethos of "freedom" has little support in Australia, by and large we seem to be very accepting and tolerant of, or even demanding of, levels of Government imposed legislated control, that would be anathema in the US.
Indeed, all too many Australians seem to feel uncomfortable with the very idea of the level of constitutionally protected personal freedom that is taken for granted in the US. The general approach to defamation in the US is one example, if you are any kind of a public figure, politician or similar, you just have to wear the most outrageous slurs. The recent inquiry into media content here would never happen in the US, the First Amendment guarantees of freedom of speech is taken very literally by the US High Court.
Further, "they wouldn't have made those accusations if they weren't true" or "where there's smoke, there's fire" are very common mindsets, particularly in aviation, were practitioners are very ready to believe their worst about their peers.
Having said all that, the "say nothing" advice is good, and police or other "trained investigators" here use all the same techniques as shown in the video, in pursuit of successful prosecutions, don't give them a free kick.
There is a famous case, years ago, of a DH 82 very publicly flying under the Sydney Harbour Bridge. DCA ( I think it was at the time) demanded that the pilot of the aircraft admit he or she was the pilot. "Nobody" saw who climbed into the aircraft, or who climbed out, so DCA had no "independent witness" proof of the identity of the pilot, only a potential admission by the pilot. There was no dispute over the identity of the aircraft, or its owner.
The alleged pilot said nothing ---- and I mean nothing. He or she did not deny they were the pilot, so they could never be accused of giving false evidence, they just said nothing, zilch, naught. DCA never succeeded in establishing the identity of the pilot, and the matter was finally allowed to die.
As far as "air safety" is concerned in Australia, "air safety" is such a holy cow that even "proof beyond a reasonable doubt" all too often produces "facts" that would only be accepted in an aviation environment as "evidence".
Tootle pip!!
PS: One of the sad things I come across, from time to time, is "somebody" being so keen to assist CASA investigators, to try and show what reasonable persons they are, that they wind up admitting guilt to things that CASA didn't know about. Not keeping it zipped can prove to be very expensive --- don't back your chances in a field where you are a naive novice.