Additionally, there are many factors that can be used to determine the risk of natural birth.
However, there was a significant difference in the reasons things went wrong. Because in a hospital you're more likely to receive unnecessary treatment due to the "cascade of intervention"; and interventions such as C-sections have inherent risk. While at home, you're more likely to have an actual emergency.
Mostly the advice we got was, if you have a medical condition that increases risk, then go to a hospital or a birthing centre. But if not, and you live reasonably close to a hospital, home birth is quite safe.
I am speaking from personal experience with births in one of the biggest US cities in the last five years. Anecdotally, I think that some less-dense areas have better CNMW practices and more access to midwives due to traditionally less access to hospitals, but it seems very variable.
C-sections are scheduled in advance (sometimes over a month in advance) because the American medical system has optimized for cost reduction (which includes extreme risk aversion) rather than patient outcomes.