I agree with Eema completely.
I think that the biggest weakness we have to date in any comparison data of "out of hospital birth with a CPM" compared to "in hospital birth with a Dr or CNM" is a lack of a good comparison that starts at the beginning of prenatal care between the two groups.
The authors of the 2005 BMJ study have suggested that care with a CPM may reduce the rate of prematurity, and since complications associated with prematurity are a major cause of neonatal death in the US, that could significantly affect the comparison. Dr. Amy asserts that there is no proof that care with a CPM reduces prematurity...and she is correct.
Further, I believe that the demographic choosing homebirth is more likely to include women attempting VBAC and grand-multiparas than the hospital birth population, which introduces risk. Dr. Amy asserts that the hospital group would contain some levels of risk not seen in the homebirth group such as Gestational Diabetes and pre-eclampsia; however these women do often start in CPM care (and sometimes do remain, depending on the severity of symptoms) and so I think it is unwise to discount those risk factors in the "planned homebirth" population.
I wish there were a good way to do a study that matched women planning homebirth and planning hospital birth but eligible for homebirth at the start of prenatal care and follow them through birth to see outcomes. Even better would be to follow them through to their second birth, since one of the claims of homebirth advocates is that birthing at home reduces the risk of primary cesarean--which if true, would reduce the risk to future pregnancies. Such a trial would be extremely difficult and expensive though, and likely could only be done as a retrospective study.