Essentially what this sentence says is "the people that don't fit my stereotype are not the image that comes to my mind when I hear ${word}." While this is definitely true (it's more or less the definition of a stereotype), it's not a refutation of OP's point that homeschooling is more complicated than your stereotypes would have you believe.

Yeck gross bleck! Religious zealots!

Rich people do homeschooling :

Oh how jealous I am Bartholomew, I wish I could have a private tutor like yours to teach my kid all of the great languages, and look the Au Pair is bringing in the lunch!

If somebody's rich enough to provide a better education to their child despite the economy of scale advantage public/private schools have, then homeschooling can be advantageous. If somebody can't do that, then they're just abusing their kid.