You're right. The reports do sound excessively weird. That almost always means we are missing some important information with which we might be able to better understand the situation. For a conspiracy to be the explanation you would have to have three police officers with the personalities of serial killers that somehow trust each other and work together. While nothing is impossible, that comes awfully close.
Another slightly less impossible alternative is that one of the officers took the lead and intentionally killed the guy and the other officers followed his lead. They either couldn't see clearly, or stress of the situation gave them tunnel vision and combined with the anxiety of the situation, they followed the one officer's lead.
A more likely situation is incompetence. The simplest answer is usually the correct one. They were told the guy had a gun, and under the stress of the situation one or more of them saw what wasn't there.
As for being untrained... you would be justifiably appalled to know the general level of competency of a lot of officers concerning hand guns. And since most officers never actually face an armed criminal it is hard to know how they will react when it happens, or when they think it happens.
For a conspiracy to have occurred the three would have been willing to work together to randomly commit a murder in plain view of the public and in plain view of security cameras without planning out the details or even having any kind of idea of who they might kill. A conspiracy that plans to not plan? Your suggestion of premeditation boggles the imagination.