I am going to take another run at this - it may be that people disagree with me, which I am used to, but it may be I have not expressed myself clearly.
If the story is: “Fallon seems like a nice guy on TV, but in reality he is a mean jerk”, then yes, they do have that story. I am not against anonymous sources (if the reporter and outlet are credible), and the story cites many current and former employees agreeing that Fallon has been a jerk, or that working for him was not as fun as they had imagined it would be.
However, that is not really the story the article is selling. The actual story is: “Fallon is an alcoholic who is often either drunk or hungover at work, making him a toxic (not just mean) employer.” While this is the story they are really telling (its the only story that justifies a long expose, and the splash they obviously expected to cause) this is the story that they do not have.
They do not have any source that establishes that he was drunk or hungover at work, just suspicions. They imply he is frequently affected by alcohol at work, but don’t specifically state how often he is impaired. They cite sources who claim extremely serious harm caused by Fallon (that he is responsible for suicidal ideation or intention, that he caused panic attacks, that he inflicted harm that required formal psychiatric treatment) but again do not describe anything that would remotely be likely to cause such effects (I can state pretty categorically that people do not literally want to kill themselves because their boss wrote snide or sarcastic comments in the margins of some written product they submitted).
If the story they wanted to tell was just that the real Fallon is a jerk, unlike his persona, then a competent editor should have red pencilled all the innuendo and suggestion about his being a toxic alcoholic. If they wanted to tell the toxic alcoholic story, then they should have held it until they had adequate support.