I have no doubt that there would be fewer complications and c-sections at a birth center, but I think that looking at statistics is misleading. For example, I have been researching hospitals. The more affluent hospital has the only midwives within 75 miles of me. All of the doulas I have found mainly attend births there. It has two cloth diaper stores that teach natural birth methods. So you'd think lower c-section, right? Nope, its much higher because all the high risk mamas go there, too.
So I think you are right, OP, in that I would want to read the actual study before I would let it influence my decision. It doesn't influence me because we have no birth centers anyway.