Yeah, the intention to treat design is a particularly nice touch, not so common outside of biostatistics. They also compare the full cost of Montessori vs. plain ol', not the cost to the state, which could otherwise have given the Montessori schools (which are in wealthier neighborhoods on average) an unfair advantage if they have a lot of parents chipping in with donations and help. I've skimmed through the methods section and it does seem like they've gone to great lengths to allow for a fair comparison.

That doesn't necessarily mean the result will extrapolate, though. It seems plausible that teachers in Montessori schools are more motivated and knowledgeable than the average teacher and have made a conscious decision to teach in such a school. If every public school were to become a Montessori school, you would still get the cost savings (student-to-teacher ratios are higher in Montessori!) but you might lose that above-average enthusiasm and expertise and so the learning gains might not carry over. It's just really hard to know whether something might generalize in the educational sciences.