Not true. The AF Safety Center trains safety personnel and they most certainly do train folks to offer privilege for personnel directly involved with the mishap. Whether your MAJCOM practices this is another thing.
Privileged statements lose their promise of confidentiality if the the witness lied, or if criminal acts were carried out. Other than that, no.
AFI 91-204
3.3.2. The Air Force does not use privileged safety information as evidence for punitive, disciplinary, or adverse administrative actions, for determining the misconduct or line-of duty status of any person, in flying evaluation board hearings or reviews, to determine liability or liability in claims for or against the United States, or in any other manner in any action by or against the United States.
You're mixing apples and oranges here. Safety isn't going to say a thing about council because they don't have anything to do with legal proceedings. And as to the secret menu, that's BS as well - not what's taught to safety folks, but - again - it may be a MAJCOM specific thing.