You're right Katelyn's Mom. What the other schools are saying is that their staff have been trained and certified by one of these institutions. Some of these schools can be excellent - others quite dire. Even within an officially accredited school though, you can find huge disparities between the standards of teaching like in any other system.

Although I have many good things to say about Montessori (my two boys have both had great experiences), I am still conflicted regarding a system that has very little in the way of accountability. It's kind of a matter of 'faith' and whilst your kids are doing well that's easy enough, but when you have concerns it can be very difficult to get a straight answer.