I had a similar impression decades ago. I think most people did.
...however I am re-considering that position.
It may depend on the school. That the Montessori name is used doesn't guaranty that the methods are used.
RE: Montessori.
In truth, the hippies brought her name back in the 1960s. Thus your associations.
She died within a year of Dewey, circa 1952. The part of the story I like happened all the way back in 1914, when the Dewey Gang mugged the nice Italian lady and destroyed her rep. Google “DEWEY VS MONTESSORI—THE FIGHT OF THE CENTURY.”
She was the real deal; and Dewey was a quack socialist. Thus my loyalties.
Here’s how article starts;
Here’s why:
I’ve been studying Rudolf Flesch, the reading wars, the ed wars, John Dewey, and all points in between. Along the way I learned a lot about Montessori, and her losing, bruising battle with America’s top educators. Mainly, I learned that she deserved to win....”