degrees of privatization in K-12 and success in Math and Science

Apparently, many of the countries with higher scores on science and math have degrees of privatization. Relying on the 2012 PISA data (from a 2015 Pew Foundation report—the most recent available?), many countries beat us in Science and esp. in Math. Of those, the Friedman Foundation lists 11 countries that have vouchers or tax credits—and beat us in both subjects. Wikipedia does not provide a full list on vouchers, but a comparison there would seem to yield at least that many. (Sometimes, you have to dig deep to get an answer-- e.g., in Singapore.) 

Many or perhaps all countries have “charter schools” of some sort (whether they label them as such). In any case, I’m not at all sure how it could rankle a supporter of public schools—to give more autonomy to public school teachers and administrators and more choice to parents and students in public schools. 

I should also note that this blog post is not that helpful. 
--It's predicated on the usefulness of international comparisons-- and even, prioritizing them over domestic comparisons. 
--It's predicated on univariate analysis of a complicated (sociological and economic) phenomenon. 
--It ignores basic economic theory on the value of competition over monopoly power-- for consumers and society (although not producers!). 
--It ignores a small, well-done empirical literature which indicates modest gains from injecting even small amounts of competition into the market for K-12 education.
--It doesn't mention the public's love for the GI Bill-- educational vouchers for college students-- while noting the mixed bag of support for educational vouchers in K-12. (The most likely explanation for this is the crony capitalistic support for the K-12 status quo.)