The hospital will most likely quote you a British study that showed women were actually more likely to PPH after a natural 3rd stage. The study was very flawed, as "natural 3rd stage" actually meant no drugs but cord traction. Cord traction is a really bad practice the placenta can take over an hour to come away but hospitals like the birthing room cleared up and out asap, so they tend to "hurry things along" hence tugging on the cord, not allowing nature to take its course and interferring with a process that usually a body is perfectly capable of doing. Synto can be a great drug in teh case of PPH, but really shouldnt be used as routine.
If you do go for a natural 3rd stage, ensure that what you actually mean is...leave me alone, hands off my cord! If they tug, you are certainly more likely to end up with problems. Its really your decision, and if you request not to have synto routinely, they really have to respect it, whether they like it or not.