If those in the military continue to investigate each other, I really have no hope of confidentiality. Moreover, it's not limited to military justice or the military police. I have experienced it in a medical situation too. Confidentiality is often violated.
So my only recommendation is for matters to be handled and examined by people who are not in the military. Now, I don't see why there would be breaches of confidentiality along those lines, but, if the military continues to head up the investigations, there will always be emails and phone calls spreading the news and the rumours, because that is the military world we are in.