Yes, you're right, like I said in my other reply, I'd assumed the parent poster's engagement with the agent had been trimmed down for the sake of the story, that there was more substance they left out because that was the overall thrust of the story.
And I think you're also right that they'd do some investigation, but I imagine the investigation would be over very quickly. This "people are uploading filth to my website" situation isn't so uncommon like it once was (back in my day, sonny!!).
The chance that that individual is trying to buddy up to the FBI in order to escape detection is more of a Hollywood fantasy than how real life would play out. These agents are human beings too, and they know that if someone's coming to them to ask for help, they're all on the same page.