Western medicine treats pregnancy and childbirth like a disease. So, yes; I do think they probably get delivery wrong.
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2742137/
"The rate of perinatal death per 1000 births was 0.35 (95% confidence interval [CI] 0.00–1.03) in the group of planned home births; the rate in the group of planned hospital births was 0.57 (95% CI 0.00–1.43) among women attended by a midwife and 0.64 (95% CI 0.00–1.56) among those attended by a physician."
No offense, but the data says you're wrong.
A comprehensive study in Oregon found death rates 6-8x higher in home births than hospital births: https://olis.leg.state.or.us/liz/2013R1/Downloads/CommitteeM....
See also this meta-survey of the literature: http://www.ajog.org/article/S0002-9378(10)00671-X/abstract ("Less medical intervention during planned home birth is associated with a tripling of the neonatal mortality rate.").
Up until I think 10 or so years ago we had one of Europe's best delivery success rates with that.
After that it seems that hospital deliveries became a safer choice and we've had relatively bad percentages since then because we culturally still value home births highly.
"Studies of planned home births attended by registered midwives have been limited by incomplete data, nonrepresentative sampling, inadequate statistical power and the inability to exclude unplanned home births. We compared the outcomes of planned home births attended by midwives with those of planned hospital births attended by midwives or physicians."
and
"We included all planned home births ... and all planned hospital births meeting the eligibility requirements for home birth that were attended by the same cohort of midwives ... We also included a matched [my emphasis] sample of physician-attended planned hospital births (n = 5331)."
However, the increased death rate in the Oregon study is
a) localized to that state, and b) attributed to an overabundance of uncertified midwives:
> But out-of-hospital births are not as safe as births in hospitals in Oregon, where many of them are attended by birth attendants who have not completed an educational curriculum designed to provide all the knowledge, skills and judgment needed by midwives who practice in any setting.
In other words, there are a lot of "birth attendants" practicing midwifery in Oregon who aren't necessarily CNMs (certified nurse-midwives) or CMs (certified midwives) -- which is perhaps closer to the barber acting as surgeon analogy.
EDIT: Here's a rebuttal to the Wax study: http://www.midwiferytoday.com/articles/ajog_response.asp
You can't compare those numbers, they aren't the same populations of pregnant women.