I don't know what level of certainty LEOs get regarding a situation, but if there's any possibility of a bad guy with a firearm, I would expect them to err on the side of safety (their own and others).

Police officers get no leeway when deciding on deadly force. Their actions will be examined by internal affairs, review panels, often grand juries, occasionally criminal courts, very often civil court. For years. You need to be right. It comes with the job - policing is an armed service.

Do recall the 'totality of the circumstances' test. There were at least five LAPD officers within 20 or 30 feet of the suspect, with more covering every entrance/exit, and even more coming up the escalator; they were on the second floor of a department store. Whacko Walliy wasn't getting away.