We read this frequently in our newspapers: “speaking on condition of anonymity.” What does it mean? I suggest the following, but wonder what you think when you hear this expression in a newspaper or TV report:
I’d like to know what you think, but it would be great if some newspaper or magazine or TV people could weigh in. (Stephen Shields — you out there?)
First, that the source isn’t supposed to know what he or she knows, but does, and is making it public.

Second, that the source is unwilling to be held accountable for making something known, which means that person has either stolen information or will lose his or her job for making something known — in which case we are dealing with information from a source that isn’t being morally responsible.
Third, that the person reporting the speaker wants to protect his or her sources or doesn’t personally want to divulge a source or — less often — is simply making something up.