I think that it can be a bit of a red herring linking the mental resources to birth with the ease of the birth though. I know that in a lot of cases a scared mother means that she is producing adrenaline which can slow down contractions, or the fear can increase the pain.
In my case though, I was perfectly capable of handling the contractions without pain relief using relaxation and breathing techniques, I was very active and upright, and I was in a supportive atmosphere with people that I trusted. So I would tick all the "inner strength boxes" (that I actually find quite patronising BTW). But in both my deliveries I had big problems getting my babies to descend. The first time around DD1 was OP and did not descend at all, the second time around DD2 was OA and I just got her to descend with superhuman effort and purple pushing (completely throwing my "don't let me push to hard/don't let the second stage go too quickly" fears out of the water! ).
We do have babies with big heads and we do have pelvises that a comprimise between walking upright and being able to get a baby out at all, and some women are going to pay the price for that. Evolution doesn't create bodies that are optimal, it only creates bodies that are good enough. As long as enough babies survived over the years to sustain the population, evolution wouldn't "care" how many babies or mothers died.
Natural birth techniques are great to allow as many mothers as possible to deliver without intenvention, and with as little pain as possible, but it really gets on my nerves when smug people (like the woman in the article) assume that they are the be all and end all of childbirth.