The midwife I apprenticed with before I moved has started doing more of these kinds of births. Here's a brief description from an email conversation we had about two years ago:
My midwifery partner and I have done a few births this summer in which the parents did not want to be bothered with at all...no heart tones, no vag checks, etc. OK...so that's what we did. Many first time moms, too. When mom was getting away from herself and feeling out of control, I would go over to the tub, get to eye level with her and tell her she was strong and powerful, and that this is normal. She is doing fine. Then I would give her a drink (Dad, too) and give her a cool cloth...then back to couch! Same when baby was out...mom caught her own baby and sat back w/Dad to admire their son. We checked that baby was breathing without difficulty and pinking up, Mom didn't look too bloody, so we retreated to the couch again until they called us to get out of the water.We need more midwives like you!