The article you cited says: "The police officer left with a curt nod and without filing a report." And "agree[d] that this was a little ridiculous." It was officially marked a "non-event".
The whole point of the story is that it's not illegal. An inappropriately nosy neighbor caused a stir, and that sucks. But there's no reason to escalate and downward spiral the situation by countering with factually incorrect claims.
It's a record of a "non-event." It's precedent of an accusation against the mother being illegitimate, not a black mark against her. Though I'm sure she obviously wishes the incident had never happened.
Either way, though, it's still not in support of calling it "illegal" to have your kids playing outside unsupervised.
The whole point of the story is that it's not illegal. An inappropriately nosy neighbor caused a stir, and that sucks. But there's no reason to escalate and downward spiral the situation by countering with factually incorrect claims.