There could be any reason for that. The neighbor might be naive and unfamiliar with children and think it is a big deal, the neighbor might have misunderstood what the child said, or the neighbor might just be unusually fearful. The point is - if the police functioned reasonably then it wouldn't be a big deal to call them and report a walking child - not necessary, but no real harm. I see no evidence the neighbor was trying to be harmful, the neighbor just made a bad decision but could not have reasonably predicted the consequences of that decision.
Maybe another way to put it is that the neighbor did a slightly bad thing, unnecessary police call, call it 0.01 Bad. The police did a terrible thing, 100 Bad. Judges and prosecutors even worse because they failed at their explicit task - making reasoned judgments about what is right and wrong - 1,000 Bad. CPS also had a complete failure of their explicit task, but maybe it is a little more excusable because hopefully most people who reach this point in the process actually do require some intervention, call it 980 Bad.
When you say that the neighbor is also to blame, it's kind of true in some meaningless technical sense. The neighbor did something slightly bad, but it is so slightly bad as to be totally inconsequential in the broader sense. If you were to try and minimize the badness here you should focus on the justice system, CPS, and the police - and you would basically never get to the neighbor because you could never optimize those other systems enough for the neighbors small fault to be consequential.
The failures here are all of the form "You incorrectly invoked system X. That was a mistake because X is totally broken!" The neighbor incorrectly called the police. The police incorrectly arrested the mother invoking the courts, the courts incorrectly penalized the mother and invoked CPS. All of those systems are completely broken and the solution is not to minimize calls to them, but to fix the systems.