So I went hunting from that link, since scoring so highly simply doesn't pass the sniff test. The reference is an academic paper full of weasel words ('many studies show' type stuff), and that particular commentary (1,952 students bit) came from a book by Brian D. Ray, a not exactly neutral proponent given he is the president of the National Home Education Research Institute. I didn't find a relevant excerpt from the book, but I have found an infographic[1] based on it and other articles.
Turns out that it doesn't matter how poor or uneducated the parents, the students still perform in the top 20%, including maths and science (the latter being particularly suspect given the strong showing of fundamentalist religion in the homeschooling world).
Going back to the reference paper and pulling another reference[2], it clearly states in the abstract that while they found significantly higher rates of performance in the home-schooled kids, they also had a significantly more educated parents and significantly higher family income... and also clearly state that since their experiment wasn't controlled, you shouldn't read too much into it.
These numbers in that link are cooked. They're nonsense. That link is using weasel words, apples-to-oranges comparisons, and pulling info from non-neutral parties. Is home schooling better or worse? Well, it depends; it is better for some, and there are certainly some myths. But that link is cooked.
[1]https://www.nheri.org/HERR.pdf
[2]http://epaa.asu.edu/ojs/article/view/543
