How exciting, MT. That went pretty quick! I know exactly which Polish mother you’re talking about because they participate in our playgroup.
There is the possibly of infection, as d’girl says, but there’s really no time limit on that. It could be hospital policy though so you might want to ask your doctor if it is, if that’s important to you. This worry about infection is why some doctors tend to rush mothers through labor and delivery, that and maybe they have somewhere else to be 
Hmmm, you might want to clarify what you mean by the above MT. Was your SIL’s bag of waters broken to start labor? Or did the water bag break and then the doc wanted to speed contractions up so they gave her drugs? There’s a difference. You don’t want the doc to break the bag because that water provides a “cushion” during labor, making the contractions more manageable. And then getting pitocin to stimulate and “speed up” contractions isn’t recommended by The Crunchy Ones because they tend to be much more powerful and intense, resulting in a more tired and frustrated mother, sometimes leading to other interventions. Remember I’m not a doctor or midwife but I think it should be avoided unless you’re absolutely sure labor isn’t “progressing”.
Different women will progress at different rates. You have some women who might be in “labor” (maybe not active labor but having contractions) for several days, some get to transition and have a very long rest period (again here is where some doctors think it’s just not progressing when more likely, her body is just taking a much-needed break for the pushing), and then there are those lucky mamas who spit them out in 2 hours, start to finish. Sigh.
Anyway, to answer VAB’s question, there are a few doctors I know of who do support natural childbirth. Jean Chang and Bernice Chen at Chung Shan are two doctors who are pretty popular, and the older gentleman who attended my third child’s birth at Adventist (he’s no longer there though). I’m sure there are others that Chinese families see.
There is one male doctor who is involved with the La Leche League who, I’ve heard, is supportive of home birth but he’s not in Taipei; it might be down south. Contacting the Taiwan Breastfeeding Association www.breastfeeding.org.tw might get you some leads.
I’ve had three unmedicated births, two here, in hospitals. One last thought, I learned recently from another Forumosan that the pastor’s wife at Grace Baptist Church has had homebirths here. You could always call and see how she was able to arrange this.
Hope this helps some and I didn’t just make you more anxious.