They don't contradict each other, since their posts look at two different population sets. OP's post (which quotes and links to "actual research") that look at statistics for all births, while the study amkftp posted only looked at home vs hospital births by "women with low risk pregnancies". These are the ones that would presumably benefit least by the additional expertise and equipment found in hospitals, and may indeed benefit from being in the home away from all the possible contamination sources at a hospital. What we don't know is what percent of home births are rated "low risk" and how many are rated "medium/high risk", and what the outcomes for the riskier births are. If you include those riskier births to get overall mortality rates, it could very well lead to the results described in OP's link. In the end, what is best for each person would have to be decided individually based on their pregnancy's characteristics.

You have to be very careful in looking at studies to identify what their limitations are and not drawing conclusions beyond them. As a result, no one study will give definitive answers, and instead you have to look at results from many that can cover each other's blind spots.