The 1966 book by Truman Capote, about the 1959 murders of four members of a family in Holcomb, Kan., is supposedly a "true account" and is commonly referred to as "true crime" although the book is in part fabricated.
Capote himself called it a "nonfiction novel" but perhaps should have just called it a novel. See this Wikipedia article for examples of where Capote allegedly invented some parts, including a 2013 allegation. The book is subtitled "A True Account of a Multiple Murder and its Consequences," yet it is not completely true and, by the standards of journalism, it lacks integrity.
Journalism schools have traditionally taught college students that accuracy is most important. Even though "In Cold Blood" was written during the 60's, when flowery "new journalism" was popular, that didn't make it right for Capote to invent part of "In Cold Blood" and then call it true and nonfiction. Journalists of today might purposely include factual errors in their reporting, perhaps because of the time constraints of meeting a deadline or because they are too lazy to double-check, but it still isn't ethical.
Capote was not from around here; he was from the South and the east coast. I think that for accurate true crime I would prefer "Three Bodies Burning," a recent book about Omaha.