We don't really know why he did it. I just think it is wrong to assume he was making a silly mistake, when there is another plausible explanation.
Just my opinion but I think it is much much more likely that he was trying to quietly reload.
Other LE across the country have put their brass in their pockets in the middle of a gunfight. Some died as a result. The cause was, without question, traced to their training were they TRAINED themselves to put their brass in their pockets rather than practice speed loading and police their brass afterwards. Instructors did nothing to correct the practice. As Charlie points out, pocketing their brass may have been a requirement with some agencies.
The placing of brass in the pocket is a rote function, done without thought, while the mind is concentrating on other things. I'm trained to jump in my car, start it up, release the emer. brake, put it in gear and head out. Don't think about any of it. I'm TRAINED to do it without thinking, like all of us.
I see citizens training themselves to get killed in gunfights all the time. Like ejecting their magazine into their hand and putting it in their pocket.
But not where LE is concerned, since they've long since updated their training and made speed loading a part of it.