Let's take this a bit further. We are never going to be able to eliminate all ignorant law enforcement regardless of training, that's just not realistic. Or prosecutors. Or...
I mean, this is a case in point (all of them were dumb or unwilling to admit to error in judgement), and I am sure you've seen plenty yourself: I don't know a single person who hasn't first-handedly experienced a dumb police officer (not saying they all are, but some certainly are).
If we accept that we'll never get everyone to be perfect, we should accept that we rely on everyone to not be dumb. It starts with your neighbour and you.
If I was the parent, I'd include the neighbour in my damages (emotional, reputational and lost income) suit along with the police and all the other institutions that didn't put a stop to this. Provided the parents can win anything in court, which I am not even sure about.
If the neighbour was really worried, they could have accompanied the kid to the house and had a chat with the parents.
In this case, we want to avoid situations where parents are punished for their entirely reasonable childcare decisions. We're never going to be able to eliminate all ignorant busybody neighbors; that's just not realistic. So the law needs to be structured (and law enforcement trained) to ensure nosy neighbors can't cause damage like this.
And I think fixing the law enforcement response will actually fix some nosy neighbors: law enforcement telling such people that their report is incorrect and inappropriate will have the effect of reducing the incidence of such calls in the future.