Limited hangout is intelligence agency jargon for a form of propaganda in which a selected portion of a scandal, criminal act, sensitive or classified information, etc. is revealed or leaked, without telling the whole story. The intention may be to establish credibility as a critic of something or somebody by engaging in criticism of them while in fact covering up for them by omitting many details; to distance oneself publicly from something using innocuous or vague criticism even when ones own sympathies are privately with them; or to divert public attention away from a more heinous act by leaking information about something less heinous.
The term entered the popular discourse around the time of the Watergate scandal, when Richard Nixon and several advisors were caught discussing whether to release selected bits of the Watergate scandal to obscure the actual role of the White House in the burglarly.
Conspiracy theorists in their paranoia tend to be over-sensitive to seeing "limited hangouts" where none exist. For example 9/11 and John F. Kennedy assassination conspiracy theorists are notoriously fractious, often accusing each other of being part of the cover-up by only revealing selective information.