Well, look at the Iran-Contra conspiracy, since that's a conspiracy that virtually all historians acknowledge. Most of the participants had no idea that they were aiding a conspiracy, and most of them did not grasp how their actions fit into the larger picture. Some of them had some idea, some understanding that their actions might be illegal, but they felt that they were just following orders, that it wasn't their place to question things, and that their superiors must have had good reasons for giving the orders. Others had no idea they were doing anything wrong, much less that they were aiding a conspiracy, until the Iran-Contra affair was exposed.
The reason that all the medical personnel who were involved with the autopsy were forced to sign strict and severe secrecy agreements was that only a few of them were knowingly aiding the cover-up of the facts about JFK's wounds. The vast majority of them were just doing what they were told, and many of them said they were very surprised that they were forced to sign secrecy agreements and were threatened with such dire consequences if they violated them.
The standard line that was used on many innocent participants in the cover-up was that the truth about JFK's assassination had to be concealed in order to avoid a catastrophic nuclear war that would kill tens of millions of people.
The JFK assassination conspiracy involved perhaps 20 high-level conspirators, a few dozen second-tier conspirators under them, and perhaps 10 high-level accessories who were aware of the plot, who wanted JFK dead, who did nothing to prevent it, and who did what they could to help cover up the crime. I think J. Edgar Hoover was an accessory. I think David Atlee Phillips was at least a second-tier conspirator. I think James Angleton was a high-level conspirator. I think J. Walton Moore was at least a second-tier conspirator. I think David Sanchez Morales was a second-tier conspirator. I think one or two of the Joint Chiefs of Staff were either accessories or high-level conspirators.
