Sounds like a potentially loaded question to me, when you consider how very much emotional valuation we place on the term "natural birth". Would we use the term "unnatural birth" to refer to anything else? Personally, I prefer more specific descriptive phrases instead; such as unmedicated vaginal birth, vaginal birth w/ IV pain meds, etc, when it's appropriate to use such descriptions. Other times, of course, it's just more practical to stick with the phrase "natural birth". And if we're gonna be sticklers on that, well then anything other than unassisted, unmedicated vaginal birth would be something less than natural, wouldn't it?
Splitting hairs, of course. If you had to pin me to the two answers in the survey, I guess I'd have to say that no, the medicated birth is not "natural". No offense to anyone who might perceive that negatively. It happens to be what I had w/ three of mine though (a dose of IV pain meds or two), and I felt pretty "natural" about them all. Then again, maybe the hair-splitting doesn't matter to me.