The New York City police officers who shot and killed Jeffrey Johnson near the Empire State Building last week did not know that he was a lone gunman with a vendetta against a co-worker. The incident took place close to a world-famous landmark in a city that has suffered dearly from terrorist attacks, so it’s not surprising that police reacted aggressively. Still, the incident, in which innocent bystanders were also shot, raises questions about whether police were too quick to assume a broader terror plot was underway ­— and about claims by the gun lobby that having lots of armed people on the scene is the best way to stop gun violence.

The New York Police Department has admitted that all nine bystanders wounded were actually struck by bullets or fragments from two cops. This mystifying fact should result in a serious review of protocols; these officers are trained to be good shots. This was chaos in a crowded environment — an environment that ought to be controlled by law enforcement. As they review the incident, investigators should determine whether any suspicions of a larger plot prompted officers to fire their weapons in ways that would endanger innocent people.

The incident is also a warning sign. The rampage at a cineplex in Aurora, Colo., earlier this summer has prompted calls to impose new restrictions, or resurrect old ones, on sales of certain types of guns and ammunition. But gun advocates have resisted these efforts. Arming more citizens, they reason, will offer better protection from would-be shooters.

The shootings of bystanders in New York exposes the fallacy in that argument. The best-trained police officers can be in error when actually facing an enraged gunman. If even these professionals end up shooting and injuring bystanders outside the Empire State Building, how can private citizens be expected to discern an attacker from innocent people inside a darkened theater? Even if the police officers’ actions were consistent with department policy, it’s easy to imagine the kind of bloodshed that would have occurred if the public had also gotten into the mix.