This statistic I had second-hand from several sources I'd read long ago and simply took for granted. Following my usual practice, when someone leads me to doubt my sources, I dig deeper to check, and correct myself if I'm wrong. Though I've already responded to several people on this already, going back more than a year now, it eventually occurred to me I should just blog it. So here you go.
The story turns out to be more complicated. But I'll start by cutting to the chase, and then discuss. The short of it is: I was wrong on specifics. But I wasn't wrong on the general point. God still kills mommy. Just not as often as I thought. Or where and when I thought. For example, I would not have been wrong if I'd said 1 in 5 before civilization, rather than (as I did say) before modern medicine, not only because "modern medicine" is too chronologically vague to be helpful, and too geographically indiscriminate, but more importantly because such high levels of maternal mortality are only documented for pre-civilized populations (though some of the worst modern conditions come close). And no matter what the rate, obviously a baby's monstrous head is not the only thing that kills women in labor. God blasts moms away with a whole physiological shotgun of design flaws.
Now for the long of it.
 "Maternal mortality in pre-Columbian Indians of Arica, Chile," by Arriaza, Allison and Gerszten, in American Journal of Physical Anthropology 77.1 (September 1988): 35-41.Forensic examination of corpses from pre-civilized populations has found a rate of maternal mortality (as in the death of a mother during or soon after giving birth) between 1 in 4 and 1 in 7. The latter held for a population in the Andes until around 600 A.D. when maternal mortality consistently dropped to about 1 in 20. The change appears to correspond more or less with the development of cities and urban economies there, which presumably led to greater (though of course not yet sterling) nutrition and other improved conditions.
 "Deaths in Childbed from the Eighteenth Century to 1935," by Irvine Loudon, in Medical History 30.1 (January 1986): 1-41.Studies of modern records dating back to the 18th century (now an age of scientific medicine, though still lacking antibiotics) have found a rate of maternal mortality varying between 1 in 30 and 1 in 60 (though occasionally better). This gradually dropped during the 19th century, when rates more typically fell between 1 in 100 and 1 in 200, until 1935, after which rates of maternal mortality in Western industrialized countries dropped precipitously to well under 1 in 1000. In fact, in many Western nations it now approaches 1 in 10,000, and in some even 1 in 100,000. The proliferation of antibiotics and other modern conveniences has clearly made a tremendous impact.
So much for the historical parameter. The geographical one remains as varied. For example, the worst modern maternal mortality rate I can confirm is that reported for contemporary Afghanistan, which has reportedly risen to 1 in 6 (according to Pamela Constable, "Many Afghans Lost to Hazards of Childbirth," Washington Post, 6 June 2006: A10). In some regions of Africa it rises to 1 in 40 or even 1 in 20 (e.g. "African Ambassadors Seeking International Help for Women's Health in Africa" and "Maternal Mortality 2100 Times Higher In Sierra Leone Than In Ireland"). But even Africa is not homogenous. Within more prosperous countries the rate drops considerably. For example, in modern Ghana the rate of maternal mortality varies between 1 in 400 and 1 in 900 (according to Martey et al., "Maternal Mortality and Related Factors in Ejisu District, Ghana," East African Medical Journal 71.10 = October 1994: 656-60). Thus, once again, greater access to modern medicines and techniques (and modern nutrition and conveniences) clearly have a huge affect on a mother's chances of surviving childbirth (regardless of the root causes, which appear not to have changed--we can only cope better with their effects).
Which in general is the point I wanted to make...
In print I always took care to avoid numbers, sticking only to the general point, which is the same I made in Flemming's interview. In my book, Sense and Goodness without God (on pp. 153-54) I wrote that if God had actually given us a soul, we wouldn't need a brain, and if we didn't need a brain, our heads wouldn't need to be so big, and if our heads weren't so big, "fewer mothers would die in labor." Though in technical detail that's an over-simplification, it's still true. Regardless of what the maternal mortality rate was before modern medicine, whether 1 in 5 or 1 in 50, or even 1 in 500, it would still have been a lot lower without that mother-killing brain of ours. This is affirmed by Hilliary Creely and Philipp Khaitovich in "Human Brain Evolution," Progress in Brain Research 158 (2006): 295-309.
I incorporated this point more formally in my Argument from Mind-Brain Dysteleology, which I articulated in my opening statement for the Carrier-Wanchick Debate. There I listed several dysteleological attributes of the human brain, only one of them being the fact that a nice God would have given us a mind that "doesn't pose a physical threat to a mother's life or health during delivery (as human brains do, in contrast with all other mammalian brains)." Again, I avoided any specific rate of mortality and stuck with the more general fact of relative mortality. Smaller brains would save more moms.
Afterwards Ted Drange brought up a good point about this, which I should digress on here. I argued that a large cranium (relative to its size prior to evolving consciousness) is the only way you can get a conscious mind on naturalism, but a very unlikely way to get one from intelligent design. Yet maternal mortality is a partial exception to this general rule. For cranial size is only a probable liability for maternal mortality (not a necessary one), and only in certain evolutionary circumstances (such as evolving consciousness within a primate lineage). This makes it very much unlike the other liabilities I listed (such as increases in the material costs to build and maintain a brain, or brain vulnerability to injury and deprivation), which can never be avoided in any natural evolutionary circumstance, yet could easily be avoided by an omnipotent engineer. Increased maternal mortality, on the other hand, could be avoided even by a merely human engineer. All you need is someone willing to give a damn. For a race of manufactured androids or lab-grown humans, for example, could easily avoid the problem.
But accidents of evolution could also dodge the bullet. For example, an alien race that lays eggs, or carries a fetus to term externally (like marsupials), or had already evolved a sufficiently large cranium before evolving a complex brain, would avoid the maternal risks of the cranial enlargement required to evolve consciousness (though none of the other risks). For scientific reasons I suspect these circumstances will arise less frequently in the universe than evolutionary paths comparable to mammalian development on earth (e.g. eggs are not as efficient a means of storing and supplying the vast energy and nutrients required for the development of highly complex embryonic brains, trying to grow such complex embryos outside a protective womb brings its own magnification of attendant risks that reduce its evolutionary frequency, and the convenient good luck of pre-evolving a big head would be inherently rare).
But I must admit my argument might not apply to maternal mortality on all hypothetical worlds (as the question then of relative probability is more problematic). It only applies with certainty when assuming circumstances like those observed on earth. For on earth, given our confirmed history, the only path from pre-human primates to sentient humans is a path of mommy-killing brain enlargement. Unless there is an intelligent engineer in the mix. Hence the use of this item in my AMBD.
More recently I met some rather fanatic defenders of "natural" childbirth (complete with the usual condemnations of hospitals and doctors and all the trappings of modern medical care) who all claimed that women were built perfectly and have no problem pushing out babies, and in fact all maternal deaths are the result of other factors (like, say, various forms of systematic malpractice by evil men). That's exaggerated, and as much propaganda as fact. But it's also a straw man. Obviously most women get through childbirth fine, especially in the modern era of surgery, sanitation, nutrition, antibiotics, and the ever-convenient recourse to calling 911. In fact, even in the worst conditions--like modern Afghanistan or the primitive Andes--most women get through it alive. After all, even if 1 in 5 die, that means 4 in 5 live. Anyone who has a basic grasp of math can tell, even in the worst of places, that most anecdotes will turn out well.
But they don't all do. It's not all roses and mother goddesses. I once personally met a women whose vaginal canal tore during childbirth, and she would have bled to death, but for the surgeons that were conveniently around at the time. Statistics from some of the studies I referenced above show that most women who die in childbirth do so from bloodloss or obstruction, two effects that would certainly be reduced (though not eliminated) if our heads were smaller. To get the point, one need merely compare our rate of maternal mortality in the wild, with that of cats or chimps (which is certainly less than 1 in 60 maternal deaths per child, and probably far lower, judging from what I've seen, though I could find no clear-cut data). At any rate, no matter how many happy stories you have to tell, there will still be some very unhappy ones to go along with them. How many will be a direct factor of where and when you happen to live. In other words, it's a direct factor of access to improved conditions.
Oh, and of course, for many women (though not all), even if it goes well, it hurts like f*cking hell. It seems hard to deny it would hurt a lot less if those heads weren't so big. I have met some women who had no problem with the pain, but then I've met far more who had every problem with it. Of course, God says he did that to women on purpose (Genesis 3:16), which qualifies him as an assh*le. But even if we set aside compassionate design parameters (like "build it to work better so it hurts less"), and even when we add the fact that eliminating maternal mortality altogether would certainly require many more design changes besides, it's still a fact that if babies had smaller heads, they would kill fewer moms. We can only quibble about how many. But that's of no consequence to the general point. The idea of "acceptable losses" in this case is only an option for the impotent. The omnipotent can have nothing like that excuse.
Addendum: More scientific research on this subject is cited in comments by Richard Carrier on January 29 and February 12.