The Homebirth in the Hospital book doesn't address statistics specifically, but I assume physicians following that model would have similar, lower rates of interventions. (Do note that there are other things on the Village OB site, such as encouragement of continuous monitoring, that do not seem consistent with an integrative model.)
I finished the book (and the OB practice's site) feeling like a "homebirth" in a hospital is most definitely not for me (not really enough like homebirth at all!), but also feeling glad and optimistic that there are medical care providers out there who are seeking to practice in integrative ways that respect birth and women. I also am fully aware that the vast majority of American women give birth in hospitals and I think we desperately need other hospital-based healthy birth options to meet those women's needs!
I was also reminded of a section in the book Birthwork that addresses complementary care:
Parents who have quite comfortably given birth naturally and taken responsibility for their health are often perplexed by the zeal with which the medical model is upheld and promoted...Conversely, ardent natural birth activists can similarly perplex and infuriate those who have been grateful for necessary medical help their received when they gave birth in a hospital.This section also reminded me of the recent study from the Netherlands about the safety of homebirth and how their maternity care system is is much more cooperative than we see here as it promotes access to midwifery as well as a good transportation and referral system (which necessitates working, egalitarian relationships between care providers).
Like all great systems of belief, the revelations and tools of borth modern medical birth and natural birth are there to be embraced by those who choose to embrace them, and to be kindly offered to those who may benefit from them. We need to begin by negotiating the confusion that exists around the availability and right to medical help for a planned natural birth, and the availability and right to birth naturally within a medical setting. Rather than insisting on one right away, we need to appreciate that different systems of care can be complementary and helpful to one another. They can work together.