System broke?

I was at the ob/gyn's office in LA with my sister-in-law who recently got pregnant. One of the key questions and concerns of my s.i.l was that if her doctor was going to be one at the delivery room. Why'd she ask? Well, she heard stories that it is common for women's ob/gyn's not to be the one who are actually deliverying your baby unless there is ample reason for them to be there. Typically, her doctor said that you will be delivered by whoever is on duty at the time you enter the hospital and go into labor. Her doctor also said that "doctors have lives, too, so we cannot guarantee that we will always be there." I left the doctor's offic wondering if this is really how the "system" works or are women just accepting this answer without demanding what they want. I wouldn't want some stranger deliverying my baby especially if something goes wrong. What are we to do?