Yes, it is true that the leading causes of preventable bad birth outcomes are poverty and lack of access to care. However, the women in the USA who choose home birth tend to be relatively privileged! Approximately 90% of women who deliver at home with a midwife are white and approximately 90% are married, as per CDC figures. They are also less likely to have serious preexisting health problems, because women with known issues usually choose hospital care.
However, despite the fact that women who birth at home are healthier beforehand, they have worse outcomes. Much worse. The only possible explanation is that lay midwives do not provide good care.
Women deserve real health care, not lies. Poor health care is the opposite of empowering.