While the coworker is a complete nutso, I honestly don't see what the HR director did that was so wrong. While discussing salaries isn't against the law, it is certainly a way to raise lots of office drama. If his job is to keep office drama to a minimum, I don't see how pulling Clake aside and asking him if he was discussing his salary with his coworker. Obviously, the lady didn't go into details about the discussion between her and Clake, so the HR director probably wanted to find out exactly what went on that would get her so bent out of shape.
If I was HR director, I wouldn't want employees going around bragging about how much they make and what kind of expensive things they can buy with it - while Clake obviously wasn't doing this, the Director didn't know until he spoke with him. There's nothing wrong with hearing both sides of the story.