There is the issue of the patients self-selecting which group they are in, which biases the results. But these authors are aware of that and I think they did everything they could to reasonably control these biases. The finding that hospital admissions were higher for home-births probably isn't a big deal either, since the hospital-birth is already there and wouldn't need readmission.

I'm curious as to why only 58.9% of home-birth patients had an ultrasound within the first 20 weeks compared to 75.5% of the hospital-birth group.

But I agree that this article does suggest that if you are a low-risk patient that meets their eligibility requirements for home-birth, you aren't at any increased risk.