There are very strong incentives for the Deputies to paint themselves in the best possible light in this situation. I would go as far as to say there is literally no value in what the Deputies say happened. Video of the incident, uninvolved bystander reports are what's needed.
AFAIK there was nothing about the incident that anyone's got a problem with, where the police are concerned. He defaulted to using language so biased that it amounted to lying anyway. Every single time an officer fired in his story, they "placed rounds downrange", while the shooters invariably "fired indiscriminately", even when that was plainly not true from his story (he proceeds in one case to name a target and state that he's certain they had opened fire, in that case, specifically to shoot a given officer, which is the opposite of indiscriminate).
It seems like he was so set on using a kind of template for biasing anyone listening against the accused that he couldn't turn it off, even when that language made what he was saying plainly incorrect. This is in a case where he wasn't trying to defend himself or any other officers against accusations of wrongdoing. If you pay attention this kind of thing is really common when cops discuss events. Biased language that can easily slip into outright lies is built into police culture, even when there's not (direct) pressure to lie.
People can't remember how things actually happened.