This new study hesitates to say that home birth is actually safer than hospital birth (for low risk pregnancies, which most pregnancies are). But the findings can be interpretted that giving birth at home is safer than giving birth in a hospital.
It depends how one wants to define "safety." Is safety the outcome that mom and baby come out alive? Or is safety the outcome that mom and baby are alive and unharmed?
Is a mother unharmed when she leaves the hospital with sutures from an episiotomy, or a healing C-section incision? Is she unharmed when she experiences spinal headaches for weeks, months or even years after giving birth? Is a baby unharmed when he has injured neck muscles from being pulled out by forceps, or when he has a scab from the internal fetal monitor gouged into his scalp or an accidental nick from a surgeon's scalpel?
For moms birthing babies at home, these injuries aren't even possible because there has been no epidural or internal monitorring or abdominal surgery. She's 32% less likely to have an episiotomy showing that midwives are not as cut happy as the hospital birth attendants.
As for mortality rates, the study showed that the rates were very similar between home births and hospital births (1.7% or 14 in 5,418 babies). It important to note that the percentage of fetal or neonatal deaths was comparable to deaths of babies in the hospital, showing that location of birth doesn't make a difference in those cases.
An interesting note was the researchers explanation of the mortality rate in the study. They said, "Although the crude mortality for low risk babies weighing over 2500 g intended at home was 2.4 per 1000 and intended in hospital was 1.9 per 1000, when standard methods were employed to adjust for differences in risk profiles of the two groups (indirect standardisation and logistic regression), both methods showed slightly lower risk for intended home births."
To explain the technical mumbo jumbo, they were comparing results of other studies investigating infant mortality rates in home births and hospital births. They had to use some statistical analysis to fairly compare the studies and in their comparisons, they found slightly lower risk for intended home births. Suggesting that home birth is actually safer for babies too, than hospital birth.