Is it true that hospitals are not supportive of natural birth?

Not true: Unless you define natural birth as no monitoring, no intervention, no analgesics, & no alternatives if desired... I would say no. Hospitals settings are supportive provided minimal standards are followed. These standards safeguard both mom & baby. Otherwise your definition of natural birth is more equivalent to a home delivery.

Natural ?: If you truly want "natural" you stay at home and don't consult with anyone. Death in childbirth was one of the most common causes of female death before the 20th century. Monitoring and skilled specialists to improve outcome for mother and child are one of the most important changes in medicine. The idea that you can plan & enforce a self directed birth plan like a wedding can be deadly.