Police said the victim, identified by the Corona Police Department as 32-year-old Kenneth French, of Riverside, assaulted an officer from the Los Angeles Police Department outside of his hours of duty in a non-provocative attack before the shooting.
The officer, who allegedly held a young child while he was shopping with his family when Frenchmen attacked him, shot and killed two French members of his family, police said.
Lieutenant Jeff Edwards of the Corona Police told reporters right after the incident that the police thought the shooting was the result of an argument.
"After what I understood, some people we talked to apparently had a fight inside," Edwards said. "Some types of arguments resulted in a shot."
But on Sunday, French cousin Rick Shureih told the Los Angeles Times that French was non-verbal and had an intellectual disability that would have prevented him from starting a fight.
Shureih also identified the family members who were affected by the newspaper as the parents of the victim, Russell and Paola French.
Shureih was not at Costco at the time of the shooting and did not witness what happened.
Speaking of his cousin, Shureih told the newspaper: "He was a nice giant … He has never been violent in the past, he has always been very cooperative and kept to himself."
Shureih said it was possible that his cousin struck someone, but he would not have been able to say that he was sorry, reported the Los Angeles Times.
French was able to drive and cook, but could not live alone and had not spoken in recent years, Shureih told the newspaper. He also told the newspaper that he was not sure of the exact disability of French.
In a Facebook post on Sunday, Shureih shared a photo of the victim and his parents. "Do they look intimidating to you? Did he really have to shoot them all? I publish this photo because the reports on social networks have revealed them to be the suspects and the policeman out of order the victim. "
Shureih asked anyone who could have witnessed what happened to contact him.
"It's a family that was not armed and that was just doing grocery shopping," Shureih said on Facebook. "I'm sure it was a misunderstanding that was escalated for no reason!"
The police did not name the agent involved and stated that his firearm was the only weapon involved in the case.
The officer suffered minor injuries and was released from the hospital. His child was not injured, according to officer Tobias Kouroubacalis of the Corona Police Department.
CNN sought Shureih's advice but did not get an answer.
CNN contacted the Corona Police Department to share their comments on this story, but was told that no other information was in the department's press release.