Well it is obvious that whenever possible we do not broadcast other faults and problems:
Pro 28:13 He that covereth his sins shall not prosper: but whoso confesseth and forsaketh them shall have mercy.
And even in the New Covenant we are intructed to handle a matter privately at first and with no repentance then we take two or three witnesses. I am not sure if this covers the aspect of privacy you where refering to.