Coroner David Ridley said the solider "genuinely feared for the safety of the lives of his colleagues and also himself."
Linda Norgrove, 36, was kidnapped in eastern Afghanistan and died on Oct. 8 during a failed rescue attempt.
The inquest heard she died from fragment injuries to her head and chest caused by a grenade.
Her family says it does not blame the U.S. military. Her father John said Tuesday that "a series of chance events all went the wrong way."
In Britain, inquests are held to determine cause any time someone dies unexpectedly, violently or in mysterious circumstances.