For the record, and I am very far from knowledgably on this topic, so I am not debating the rest, this does not indicate that training does not work. It indicates that the specific training they provided police officers worked. That could be a result of
1) Training is not useful to increase accuracy rates. This seems unlikely to me, as most things can be improved by training.
2) This particular training does not do a good job. This seems likely to me, as if the training is done in a range, and the studies are about effectiveness in the field, there's plenty of space for issues. Kinda like if someone punches the air, or a pad, and only does that, then goes into a fight, their ability will be lacking. That doesn't mean they can't be trained, but that the training they had was missing a crucial component (a resisting partner).
3) The police officers have no motivation to try hard in the training. This seems possible if there is no rewards/punishments for how they do. If that's the case, then no matter how good the training is, only the ones who have some internal motivation would actually improve from it.
3A) if the rewards/punishments are based on the range, you've got a mix of 2 and 3. People are motivated to train the unhelpful thing, rather than the helpful thing. From what my dad (LEO) has discussed with me, at least in his precinct (and 15 years ago) this was the case. They trained on the range, and would need to get a certain score on the range, or face disciplinary action of some sort. That means that their consequences were only related to fighting someone not resisting, in a low pressure situation, which is also what their training teaches.
So long-winded point short, training likely could help if it is focused on live pressure/resistance, AND the people participating have a reason to improve in shooting during live pressure/resistance. From what I'm aware of, and the studies I've read that say similar to your point, that is not the case. I'd be interested to see studies with those issues fixed.