It seems your argument is "people act without knowing all the facts and jump to sometimes incorrect conclusions, therefore they should be allowed to shoot people"
I just wanted to add that in the USA, there are a lot of laws that vary from state to state involving brandishing or improper exhibition of a firearm--just about every state agrees that it's not okay. This article
talks about that a bit, mostly with a Florida focus, but other states are mentioned in the article. It's important to remember that in the USA, brandishing a firearm can legally be construed as a threat to a person's life and safety, so....yes, if a person is brandishing a gun at someone, the person getting a gun waved at them does have a logical reason to fear that the other person is threatening to use deadly force on them. Just thought I'd put that here after reading some of the thread.
On topic to the thread, with this firearm info in mind: just because a person "thinks" they see a gun is not a reason to shoot. One needs to know
there is a weapon. Just thinking that there "might" be a gun is not a valid excuse.
(Not going to comment on the fellow who killed the man he caught molesting his daughter--I'm not seeing that as relevant to this thread's original topic).
Edit: Changed some pronouns to make the post cleaner looking.