Channel 4's FACTCHECK blog has some background sources on these claims.
As you say, the real question is what exactly is it that causes the improvement's associated with the Swedish free schools.
One recent study the blog mentions, from 2008, suggested that the improvements were short term and not reflected by subsequent achievement in further higher education, i.e. University/college. So maybe exam results are improving but does that reflect a genuine improvement in education (whatever that really means)?
As Panda has pointed out humans do not require clothing. Certainly it is not generally socially acceptable to run around naked in many modern societies and the use of clothing has allowed humans to expand the environments they can comfortably adapt to. But to suggest that humans have to wear clothes moves your writing from superfluous to simply ridiculous.