I don't think it's ever going to be possible to separate the outcomes of homeschooling from the selection of parents who desire to homeschool, but this overall neutral study (I'm not really arguing that homeschooling is a great thing just that it is okay) doesn't find evidence of the three out of four thing that you encountered extending to the whole population. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8580227/

My honest sympathies to your friends.