I interviewed for a job there in 2005. For a hospital I was impressed by the manager, but I think she may have left and I don't know what it's like now. It did appear that, like all hospitals, it depends on which nurse you get.
My adopted daughter was born there in August. We met her at 6 hours. The nursery nurses were all great--I actually knew a few from when I worked at UMC NICU. I got a private room for our night there and threw the mattress on the floor. Nurses saw and didn't say a thing. (I wasn't comfortable sleeping with the baby on either of the beds.)
May I offer you reconsider the birth center. Even if you get transferred to TMC (I didn't,) you'll at least have a midwife throughout your labor. Since it's the nurse, and not the doctor, that is with you throughout your labor you don't want to trust it to getting the right nurse. With a midwife, they are with you and are much more supportive of what you want than most doctors.
Have you considered a home birth? I wish I'd been able to do that, but couldn't.
Created an instant family (7/89 and 5/91) in 1997. Made a baby boy 12/05 adopted a baby girl 8/08. Ask me about tandem adoptive nursing and living as gluten, dairy, and cane sugar free vegetarians. Homeschooling and loving it.