They control for schools opting not to participate; see the section under substitute schools.

I'm aware that they tried to control, but the bounds are large and open to exploitation by the countries who so choose to do so.

And the homeschool issue should strengthen his conclusion. I was just noting a factor he hadn't controlled for.

Both factors I pointed to would tend to mean that the relative rank for the US is in reality better than listed, IMO, but the wide bounds of substitution adjustment makes it very hard to be confident in the results.