All this stuff about Hillary being a "private citizen" sounds like spin to me. As if Hillary Clinton and the guy who collects my garbage every tuesday carries the same political influence.
It is not about influence, it is about what is right and wrong for the Fed Govt to do. Political parties spend millions (maybe billions) trying to find dirt on opponents, it is part of the game. Hell the Trump dossier was started by a Repub who was a rival of Trump's.
But that does not make it ok for the Fed Govt to do it for a candidate, the Govt is supposed to be neutral on such things.
Look at it this way, a HOA could legally put in their by-laws that political campaign signs are not allowed, but if the government came out and said you cannot put a political sign in your yard, that would not be legal or ok.