The real world of our memory is made of bits of true facts, surrounded by holes that we Spackle over with guesses and beliefs and crowd-sourced rumors. On the dot of 10 on Wednesday morning, Anthony O’Grady, 26, stood in front of a Dunkin’ Donuts on Eighth Avenue in Manhattan. He heard a ruckus, some shouts, then saw a police officer chase a man into the street and shoot him down in the middle of the avenue.

Moments later, Mr. O’Grady spoke to a reporter for The New York Times and said the wounded man was in flight when he was shot. “He looked like he was trying to get away from the officers,” Mr. O’Grady said.

Another person on Eighth Avenue then, Sunny Khalsa, 41, had been riding her bicycle when she saw police officers and the man. Shaken by the encounter, she contacted the Times newsroom with a shocking detail.

“I saw a man who was handcuffed being shot,” Ms. Khalsa said. “And I am sorry, maybe I am crazy, but that is what I saw.”