JS, you are never read your rights as part of a SIB (unless something major has changed recently). When something happens that warrants it, the base will form an Interim Safety Board (ISB). The ISB will attempt to collect all perishable data/evidence/etc. When I went through FSO training, we were trained to extend Privilege (as appropriate) before we conducted interviews; however, I have heard that AFSEC is now teaching "only extend privilege AFTER someone asks for it."
Bottom line: If you have not specifically been granted Privilege, be very careful. Get it in writing. Also, Privilege is only for flight and usually not for ground or weapons mishaps.
If anyone has newer information, please correct where I am wrong.