It said the 62-year-old had died from a "self-inflicted" wound on 9 March and police were investigating.
Mr Barnett had worked for the US plane giant for 32 years, until his retirement in 2017 on health grounds.
From 2010, he worked as a quality manager at the North Charleston plant making the 787 Dreamliner, a state-of-the-art airliner used mainly on long-haul routes.
In 2019, Mr Barnett told the BBC that under-pressure workers had been deliberately fitting sub-standard parts to aircraft on the production line.
He also said he had uncovered serious problems with oxygen systems, which could mean one in four breathing masks would not work in an emergency.
He said soon after starting work in South Carolina he had become concerned that the push to get new aircraft built meant the assembly process was rushed and safety was compromised, something the company denied.
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