Private schools allow teachers and administrators to cruise through with the standard highest levels of incompetence that you might see in the business world, but there's a special degree of nepotism that often exists in private schools or charter schools. It might be people of the same background working at a charter school run by immigrants from a certain country, or it might be teachers who are all of the same synod in a religion. The point is that the best candidate for a job may never get an interview, and the upwardly-mobile administrator will eventually make his/her way to the top.
In public schools, it's often the history/gym teacher who coaches that often (somehow) becomes the school leader. That's bad enough. But from what I've seen in charter and private schools, it's all about friends, favors, and family. I'm not (generally) talking about the everyday teacher, but more about administrators. Maybe contractors who work for the schools. School board members. I've seen some pretty un-talented people get hired, promoted, and recognized as stellar in a way that often wouldn't pass the smell test at a taxpayer-funded institution.