Why not turn that trope on its head. The trope usually involves brilliant leadership dealing with the schemes of evil masterminds. Vital information is said to be held due to the panic it would cause for people to know.
But the actual information would reveal that each agency is completely incompetent, meaning that the agencies have been making horrible mistakes and have withheld information to hide catastrophes that did not otherwise have to occur if the people in charge lost their jobs. And that the great threats are overblown or non-existant in order to justify the agency's existence. The PCs are actually the competent ones working inside the beuracracy to undercut their bosses in order to make right out of wrong. See the Retief series for a good example on adventures that could come from scenarios such as this.
Heh.

Sounds like a variation of "The Gang That Couldn't Shoot Straight" or the "Keystone Cops".
The Gang That Couldn't Shoot Straight - Wikipedia, the free encyclopedia
The Gang That Couldn't Shoot Straight (1971) - IMDb