Nothing unites the people of a country like a discussion filled with conspiracy theories about a perceived enemy nation! Conspiracy theories personally give me a rush, but I don't indulge too much for the sake of my sanity.
Conspiracy theories aren't all disadvantageous for the entity they are directed at, an entity with a pool of conspiracy theories trailing it won't be so worried about leaks and anonymous whistle blowers and the controversies they bring, because with no authority (unanonymous whistle blower) or evidence attached to such information it will be left in the pool and not acted upon.

The nasty ebola-chan prank made conspiracies (not necessarily true or false) about Ebola being a bioengineered virus less convincing and the conspirators look silly.

So is there a chance that agencies and other organizations sponsor conspiracy theories directed towards themselves?