Once the medicalization of birth is addressed and homebirth is normalized, then we can begin to talk about it in terms of race and class.
Fwiw, I was on medicaid for both my births and am on Medicaid currently. I never sought Medicaid coverage for the one homebirth I paid out of pocket for (the other I went through my mom's CNM practice and she helped me and paid the assistant on my behalf) because I didn't even think it was possible (or worth the hassle!). My husband is currently working on his PhD. I come from a family where three of my parents have master's degrees. I don't have any degree, but consider myself pretty well educated, all things considered.
I think that being well educated may not equal ease in navigating health care systems (who can navigate those at all??), but just an easier time finding things and having access in general to information - so whether there's talk on a message board or elsewhere, having the internet at home is a privilege that aids that, as does the ability to browse bookstores or take prenatal yoga (where I learned a lot) or any variety of ways in which information about home practitioners could be spread.
As far as I can tell, the culture of the (largely white) middle class and educated aids this in a way that I don't think exists elsewhere. Even shopping at Whole Foods or making choices to buy green - questions about health and environment are largely in the domain of the privileged and that's where we find this related information about homebirth. Certainly that's how my doula clients find it...
Otherwise, I think we completely agree, really.