There was a time, many years ago, when police officers were familiar enough with weapons to be able to tell the difference between a handgun and something else. Hell, if I had dropped the hammer every time I had an excuse during my 23 year career, I’d have buried at least half a dozen folks that really didn’t need killing. That being said, I wouldn’t take the job today.
Whether or not they can tell the difference is irrelevant. When there is an opportunity it must be seized. It may be weeks before another opportunity arises.
The responding officers were primed for a 'man with a gun', likely cranked up on their own adrenaline when they got there.
The neighbor should be chewing crap at least as much as the officers, imho.