I'm a nurse, and if I was assisting a delivery I'd probably choose to pretend I didn't see the camera. A birth is a monumental event and certainly worthy of being caught on film. I could see where they might ask for the camera to be turned off if there were complications. Fortunately I don't work in labor and delivery.
I work with post op patients though and recently had a patient who was struggling to take a photo of his knee incision while in bed and propped up on his elbow. I was more than happy to take the photo for him when he asked for some assistance. It's the first and only time I've ever used a camera phone! :o