The five “bad shoots” included cases in which an agent fired a warning shot after feeling threatened by a group of men, an agent fired at a weapon lying on the ground to disable it during an arrest, and two agents fired their weapons while chasing fugitives but hit no one. In another case, an agent fired at a safe during a demonstration, and ricocheting material caused minor cuts in a crowd of onlookers.

Image Luqman Ameen Abdullah Credit... Ron Foster Sharif, Muslim Alliance of North America, via Associated Press

Four of the cases were in the mid-1990s, and the fifth was in 2003.

In many cases, the accuracy of the F.B.I. narrative is difficult to evaluate because no independent alternative report has been produced. As part of the reporting for this article, the F.B.I. voluntarily made available a list of shootings since 2007 that gave rise to lawsuits, but it was rare for any such case to have led to a full report by an independent authority.

Occasionally, however, there were alternative reviews. One, involving a March 2002 episode in which an agent shot an innocent Maryland man in the head after mistaking him for a bank robbery suspect, offers a case study in how the nuances of an F.B.I. official narrative can come under scrutiny.

In that episode, agents thought that the suspect would be riding in a car driven by his sister and wearing a white baseball cap. An innocent man, Joseph Schultz, then 20, happened to cross their path, wearing a white cap and being driven by his girlfriend. Moments after F.B.I. agents carrying rifles pulled their car over and surrounded it, Agent Christopher Braga shot Mr. Schultz in the jaw. He later underwent facial reconstruction surgery, and in 2007 the bureau paid $1.3 million to settle a lawsuit.

The internal review, however, deemed it a good shoot. In the F.B.I.’s narrative, Agent Braga says that he shouted “show me your hands,” but that Mr. Schultz instead reached toward his waist, so Agent Braga fired “to eliminate the threat.” While one member of the review group said that “after reading the materials provided, he could not visualize the presence of ‘imminent danger’ to law enforcement officers,” the rest of the group voted to find the shooting justified, citing the “totality of the circumstances surrounding the incident,” including that it involved a “high-risk stop.”

But an Anne Arundel County police detective prepared an independent report about the episode, and a lawyer for Mr. Schultz, Arnold Weiner, conducted a further investigation for the lawsuit. Both raised several subtle but important differences.

For example, the F.B.I. narrative describes a lengthy chase of Mr. Schultz’s car after agents turned on their siren at an intersection, bolstering an impression that it was reasonable for Agent Braga to fear that Mr. Schultz was a dangerous fugitive. The narrative spends a full page describing this moment in great detail, saying that the car “rapidly accelerated” and that one agent shouted for it to stop “over and over again.” It cites another agent as estimating that the car stopped “approximately 100 yards” from the intersection.