Fortunately, it's still up to the FBI to prove they're not lying. Now, what an American jury is willing to accept as proof is anyone's guess.
Unfortunately, you can't trust the general populace (hence, a jury of peers) to understand complex technical arguments. You also can't trust the government to offer up non-fabricated evidence.
If, at any time, a person is being watched by the gov, you can guarantee that the gov will make up any story (child porn is the easiest, I'd think) to strip you of any trust your friends and family may have had and make you look downright evil.
He probably got too close to a real exploit and they wanted to take him out.
IIRC, the real takeaway with CitizenFour was the ending where documents revealed there were open investigations on over 1.4M Americans.
Why so many? Justification of current resources/spending?