Plenty of NYC public schools provide a less structured experience than this "unschooling" family, though with quite a bit more exposure to violence and drugs, and much less academic achievement. I refuse to worry about the shortcomings of particular homeschooling approaches until AFTER the public schools, which are spending about $20K/year/student of taxpayers money, are consistently delivering a decent education. It would be misdirected worry.
I am not surprised to read that and agree that it is entirely plausible.