Actually, I can see why the lady with the back to back baby didn't get the epidural - but they should have explained better.
I had a really good, long chat with an anaesthesiologist recently - he said that (where I'm giving birth) they're 24hrs, in hospital, dedicated to maternity - that him getting there within 10 minutes was rarely actually a problem, the problem came with a) getting the epidural in safely when a woman was that far along - it's just very tricky when contractions are so close, and b) that it takes 20-30 minutes for it to kick in - and obviously more if for some reason it doesn't work and they need to top-up/resite.
If she really was already that close to actual delivery, then the chances are that the epidural just wouldn't have been in time. However that should have been explained to her, rather than just fobbing her off.
I am also shocked at the number of births on their backs though. If you're high risk, and going through all the monitoring/on back etc. then obviously your chances for an intervention free birth are lower - acting as though it's the high risk that causes the intervention, rather than the general interference contributing seems just a touch dishonest.