An example of the dilemma from President Johnson, from The Atlantic:

LBJ: Oswald Wasn’t Alone

Was President Kennedy murdered because of his actions against Cuba? His successor suspected so.

By Leo Janos
JFK ISSUE

The talk turned to President Kennedy, and [Lyndon B.] Johnson expressed his belief that the assassination in Dallas had been part of a conspiracy. “I never believed that Oswald acted alone, although I can accept that he pulled the trigger.” Johnson said that when he had taken office he found that “we had been operating a damned Murder Inc. in the Caribbean.” A year or so before Kennedy’s death a CIA-backed assassination team had been picked up in Havana. Johnson speculated that Dallas had been a retaliation for this thwarted attempt, although he couldn’t prove it.

Source: https://www.theatlantic.com/magazine/archive/2013/08/lbj-oswald-wasnt-alone/309486/

Looking back 58 years, things could have been so very different with, ah, transparent governance.