My OB and her practice were pretty into being invasive, sorry to say. I guess it depends on your OB and if they work with midwives etc. At CDH under my OB, I was immediately hooked up to pitocin, had an oxygen mask on, had a motitor attached to my baby's head while still inside me, and some other heartrate monitor on as well. Going in, I thought I would TRY a natural birth...but with the pitocin and everything that comes with it at CDH, I went with an epidural after 4 hours.
I still had an amazing experience though. I went in with an open mind, and was ready to let whatever was going to happen, happen. If you go in and tell them this is my birth plan and this is what I want, they should oblige you.
All that being said, the nursing staff in both L&D and mother/baby was amazing! I loved CDH in the end, remember to stand up for what you believe in though.