For context, my daughter is in a Montessori school in the United States. My wife was on the board of the school for a few years. We did a bunch of research before enrolling her in the school she attends.

The school is absolutely regulated by the state department of education. In order to operate as any kind of private school, they have to meet certain requirements and agree to oversight by the state. While I’m sure the details vary by state, and I’m only familiar with the requirements in my state, I think is probably pretty common across all 50 states.

For the Montessori aspect, yes, there are a bunch of “Montessori” schools that don’t really follow Montessori principles (at least there are in my area.) If you want to find a school that does actually implement Montessori principles, you have to do research (looking for membership in an association like the American Montessori Society is a good first-pass filter) and interview the school. There’s no substitute for due diligence for this.