Most coverups don't really involve people grabbing reams of documents
   and forcing them down shredders (although the Iran-Contra case comes to
   mind). Instead they often involve deceiving their participants as to
   the necessity as to continuing the coverup and the ongoing actions.
   Let's call this a JFK-style coverup.
   The most noteworthy JFK-style coverup would be the LAPD police cadet
   scandal. (perhaps the Hollywood sex scandals would be better, but I
   suppose in retrospect there is no good reason to lock a door from your
   desk)
   [1]http://www.latimes.com/local/lanow/la-me-ln-lapd-cadets-thefts-timel
   ine-20171201-story.html (excerpts for maximal understanding)
   ”When you look back, you can say, ‘Well, how come no one noticed
   that?’” said Frank. “We have a lot of young-looking officers. … There’s
   so many officers that are looking like that, we’re at that stage where
   it’s not that odd until after the fact.”
   ...
   Cain’s attorney, Bill Seki, has denied his client had any knowledge of
   the thefts. Seki has repeatedly accused the LAPD of using Cain as a
   “scapegoat” and contends other officers were aware that the vehicles
   had been taken.
   “They’re still trying to throw it at him, the easy target, protecting
   others that would have been aware of it,” he said.
   ----
   Basically he is pointing out the disingenuity of it all. I believe the
   ACLU too has been disingenuous, and so has Black Lives Matter. They
   support increased numbers of prosecutions of police brutality cases,
   and yet so many times these cases yield not guilty verdicts. Even in
   the case where a police officer shot a man because he smelled like weed
   (nevermind that burnt weed is not that different a smell from
   industrial chemicals).
   I just wonder how this could happen. It is such a mystery.
   All these millions.
   Going no where.
   Can't figure it out.
   Such a mystery.
   Insurmountable.
   Really curious.
   Don't get it.
   Beyond me.

References

   1. http://www.latimes.com/local/lanow/la-me-ln-lapd-cadets-thefts-timeline-20171201-story.html