Consider that the bodies of the Red Court vampires would have had to be cleaned up immediately, presumably by other Reds, otherwise someone would have put together "Hey, these are the same type of bodies that have been discovered all over the world as thousands of people simultaneously died with no explanation." Remember, it's within twelve hours that the Red Court died.
Either the FBI, at the very least, knows what happened, or there was some kind of weird explanation that was kludged together as a mass suicide attack that was somehow global. (Or, you know, the flood of ectoplasm that Harry unleashed from the Erlking's stalactite ceiling washed away all of the evidence before disappearing).
Personally, I like to think that Tilly gathered the survivors, sat them all down, and formed an unofficial task force, like the FBI equivalent of the Black Cats. It's not inconceivable that this guy, who was capable and canny enough to keep his crap together in the face of the supernatural, got everyone's stories straight to keep the whole thing as quiet as possible. My money is on Murphy ending up consulting for them, reversing Harry's role from the beginning of the series. I even think that they're going to show up as a vested interest in Peace Talks, either at the negotiating table or approaching Harry about what's been going on for the past few years.
Final possible solution I can think of: Marcone. He does not want the FBI poking around in the supernatural, and I believe there may be some kind of obligation to maintain the masquerade as much as possible, as part of his position as Baron of Chicago.