The phrase "a key detail" is correct and usable in written English.
You can use it when referring to an important piece of information that is crucial for understanding a situation or context.
Example: "In the investigation, a key detail was overlooked that could have changed the outcome of the case."
Alternatives: "an essential detail" or "a crucial detail".
The answer, I believe, is no, because Chinese officials are misreading a key detail.
In the book's cleverest touch, she misrepresents a key detail when describing the crime.
A key detail is the bowler hat set carefully on a small shelf beneath the official's table.
But Rosenberg had overlooked a key detail: after receiving threats, Musa had informed the government that he was not taking the posts.
Toward the end of his commentary a key detail is revealed — that many of those harming young people are other young people.
The man behind 1996 thriller The Rock has expressed his amazement a key detail from the plot was apparently used by an intelligence agent to fabricate evidence which aided the case for the invasion of Iraq in 2003.
And the excerpted portions featured in that news segment (from KGO ABC7) leave out a very key detail.
Peter Frost, a researcher at Rivier College in Nashua, N.H., showed students slides of a "crime scene," then gave them a script describing the crime, but with a few key details twisted (a copy of Vogue became Glamour, a hammer became a wrench).
In the living room, bold drama comes from a large starburst chandelier and dark blue walls — a nice reminder that a few key details can take an ordinary room to the next level.
To relate to her, a reader doesn't need to know much about her childhood beyond a few key details (she was a tomboy who rode motorcycles, is from a small Western town, is working class but educated).
Then the subjects watched the same eight vignettes again, but this time the researchers changed a few key details, having the man hide behind a tree instead of a door, for example.
