Olsen later testified that he had no memory of that conversation. So either the other cop is lying, which is extremely hard to believe since he'd have no clear motive for doing so, or Olsen is lying, and he most certainly does have a clear motive for doing so.

My best guess is that Olsen panicked and instead of thinking, he just reacted. He skipped less-than-lethal and went straight to deadly force, and on top of that he gave the order to stop and then fired "about a second" later, by his own testimony. Mr. Hill never even had a chance to comply.

Also, why was Olsen alone? Why didn't he have any backup? This is the sort of situation where, as a former dispatcher, I'd absolutely suggest a backup unit, so I'm curious if that was done. Given what they knew, why didn't they roll a crisis unit (personnel trained to deal with mentally ill people)?

I'm generally pretty sympathetic to the police and try to give them the benefit of the doubt, but... yeah, not in this case. There were so many stupid decisions here, on both a departmental and individual level. Totally avoidable.

i watch a TV reality show on A&E "Live PD" which follows police departments and shows video of the officers.
It seems often that one officer shows up first, and then may call for back up,
or back up arrives a few minutes after the first.

"Live PD is hosted by Dan Abrams, the chief legal affairs anchor for ABC News. The program features live video feeds from multiple (currently eight) law enforcement agencies throughout the United States. The departments include the Lafayette Police Department, Lawrence Police Department, Missoula County Sheriff's Office, East Providence Police Department , Richland County Sheriff's Department, Salinas Police Department, Tallahassee Police Department, and the Tulsa Police Department.

Abrams is joined in-studio by two co-analysts: former Washington, D.C. special police officer and crime reporter Tom Morris Jr. and Sgt. Sean "Sticks" Larkin of the Tulsa PD. Occasionally, the trio are joined by an officer that has been featured on the show in the field."

https://en.wikipedia.org/wiki/Live_PD#Overview

I would have insisted he put his damn gun down and realize this was a mental health issue and not a threat to his personal being. I believe two or more people could have restrained Hill while waiting for more trained back up. The way Hill moved was not the way this coward describes it. And he was naked so you can see he does not have a weapon!

He fired within 2 seconds of arriving, according to his statement.

He fired after his order for Hill to stop was disobeyed. Regardless, I'm not talking about me being a police backup. I was saying had I witnessed this happening.

I must have misunderstood your comment:
“if *I* had been his back up”

We were trained to always offer a backup unit if there was even the slightest possibility that more than one officer might be needed, and let the officer taking lead on the call make that decision. So for instance, if we were sending an officer to a vehicle collision to take a report, odds are they wouldn't need a backup officer. On the other hand, if we were sending them to a domestic violence call, we didn't even offer a backup unit, we simply sent two or more. It wasn't a choice, it was a departmental policy. In a situation like this, I'd have most definitely strongly suggested, if not outright assigned, a backup officer.

The other thing that confuses me is that even if a backup unit had been assigned, Olsen still went in alone. Given the nature of the call, I'd have expected him to stand off and wait for his backup to arrive before approaching Hill, unless the person calling 911 (or a follow-up caller) reported that Hill was an imminent threat to others or himself. If Hill was just meandering around naked and talking nonsensically, there's no pressing need to approach him right this second. Olsen could have monitored him from a distance and waited for his backup before approaching.

Just so many stupid, stupid decisions in this chain of events, and the end result was a man who was mentally ill being shot to death for no reason. Regardless of the outcome of the trial, I really hope that police department takes a long, hard look at its procedures for these situations.