According to this article [0], it's pretty vague (Montessori isn't trademarked and tough to enforce) and not all schools stick to the "classic" Montessori methods, which, I guess there's a handful of certification bodies (in the US).
To this point,
> Out of more than 4,000 so-called Montessori schools across the country, only 1,250 are affiliated with the American Montessori Society (and only 204 are AMS-accredited) and about 220 are recognized by AMI.
It was based upon talking with the people that ran the place, discussing with parents why they put them in the place (all were high achievement academic reasons), and discussing these issues with my mother in law, who was an early child development college teacher for 20 years and ran a preschool lab where they taught their college students, hands on, how to be preschool teachers.
Or is your critique more along the lines of the bigger driver for montessori outcomes isn't the montessori methods, but the affluence of the families?