Instead of telling the world about the monsters that have invaded the Indiana suburb, they opt to craft a faux conspiracy in which Hawkins National Laboratory and the Department of Energy covered up the poor girl’s death after exposure to a chemical asphyxiate.
Once the truth (or at least some version of it) got out, Barb’s family received an abridged (albeit still comforting) version of her death, and Hawkins could adequately mourn her.
Taking the tape to disgraced journalist/conspiracy theorist Murry Bauman, they found a way to cut the audio together in a way that confirmed the government’s guilt in Barb’s death — while also not forcing the idea of the Demogorgon or The Upside Down on a potentially unwilling public.