If you are told that your facility provides 24hr coverage and it makes you feel better to know that someone is there while you are, they darn better show up as soon as you are known to be in labor. I get really po'd that there is a double standard, it is soooooo important to be in a hosp. to labor and they want to drag their feet because it is 3am, I don't think so! It is your right to ask for their presence in the hosp. The fact of the matter is that if a rupture occurs and your OB is there then an emergent c/sec can be done much faster than 20 minutes, I know because I have seen them done. I have also seen a c /sec done under local to save a baby, and that wasn't fun for anyone there.
I am not trying to scare anyone, but you should be supported in your plan.