You are right. Way too many Americans could listen to Obama speak for 3 minutes on taxation and simple economic effects, and then listen to Thomas Sowell speak for 3 minutes on the same subject, and probably not understand either one of them but strongly believe that Obama is the more intelligent of the two. I think most Americans are incapable of understanding most of the content of the Rush Limbaugh show. I also agree with you on the role public education plays in this, but I have no idea how to turn this around. Home schooling kids is not a solution once the adults themselves reach this level of ignorance.
Home schooling isn't reliant on what the parents know or don't know. Almost all home schoolers use materials from outside sources, some free some not, but there are numerous curriculums available and they are not unstructured do what you want programs. There are a lot of networks for home schoolers as well.