Well I won't defend a situation I am not personally familiar with so you win that one. Keep in mind that there are many unruly 5 and 7 year-olds attending public schools too. The parents are still the parents after all. Discipline problems, which it sounds like they were the main issues with those young kids, are not solved by plopping them in a desk and saying "sit" in a room filled with 30 kids to 1 adult anyway. Perhaps the public schools are being saved from two more problem children. The influence of bad parenting is a favorite excuse given by public school bereaucrats for their need for more and more and more money. Apparently bad parents are a problem for all kinds of schooling. Fortunately lousy parents don't usually choose to home school.
These kids were depressed. If you'd plopped them in desks in a crowded classroom and said "sit", they would have done just that, for as many hours as it took until someone said "stand up". The little girl would have sobbed a little now and then, but she also did that when she came to the office on "Take your daughters to work" day -- chose a spot under her dad's desk to sit by herself quietly, and after a while was heard sobbing, without ever trying to talk to her dad or anyone else to get attention, or trying to go do something, or asking if she could go do something, or even moaning the time-honored "I'm bored". It was kind of scary, especially since her behavior had been much more normal when I saw her about a year and a half earlier, during the only year she attended school (public kindergarten).
Parents with mental illness of any kind pose a challenge to the idea (which I basically agree with) that any parent should be free to choose homeschooling without interference. In cases like this one, I think it was less a matter of reasoned choice, than of the mother being too depressed to get the kids out of bed, dressed, and out the door in the morning (I don't think she was getting herself out of bed very regularly). I hope these children were eventually sent back to school, where at least they could get some exposure to other children and adults. I suspect they were, since after the father went on mental disability leave, he must have been required to see a psychiatrist and/or other mental health professional regularly to continue to qualify for benefits, and such a professional would certainly have been concerned about the children.