A safety investigation has no legal authority to do anything, that is what an AIB is for. Either you talk to the IO, get privilege, and have faith that they system will work and bros will learn from your mistakes. Or, you don't talk to the SIB, the IO has to either A) Be really good and figure out what happened on his own, or B) nobody ever knows and whatever happened will repeat itself, possibly with a deadly outcome.
If what Day Man is saying is true...because in reality him saying that the AMC/CC used privilege to make a punitive decision is pure speculation, then I would hope there is enough integrity in the safety system that people are going to be fired and answering questions about a breach of privilege.
Bottom line: we have privilege so that we can all learn from each others mistakes and make an inherently dangerous profession a little more safe. Get your privilege statement (you will always get it in writing because you are required to sign documentation), talk to the IO, and have faith that the system will have your back.