Perhaps by Ajog (unfamiliar) you mean ACOG? They recently did put out an advisement and, yes they are probably picking and choosing to suit their case.
Unlike in the UK, most US women give birth in a hospital using an obstetrician (who is really more like a surgeon than anything else), not a midwife. Hence there is a financial incentive for ACOG to keep women in these hospitals. A normal vaginal non-medicated birth in a US hospital can easily run $10,000. A home midwife might charge $3000. I found out from my insurance that they would have covered that $10,000 in entirety had I chosen to go to a hospital, but they are only paying my midwife $2,200. ACOG needs to make homebirth look unacceptable not just to mothers, but to their husbands, their families and their insurance companies - and perhaps even to the lawmakers (as homebirth is still illegal in some states and I'm sure ACOG would love to see that list expand).
Anyway getting to the data, from what I've seen, when studies are done on "homebirth" they include all births NOT in a hospital which means the data lumps planned homebirths using competent midwives together with unplanned homebirths (accidents) and worse, women who completely ignored their pregnancy or were actively self-destructive throughout (drug addicts for example) and had zero prenatal care. The studies on actual planned homebirth are so small in the US (I saw one that had 29,000 women in it) compared to the number of hospital births they are compared against (more like 1,000,000) that any small statistical anomaly looks like a huge trend. There just aren't enough planned homebirths in the US to do any sort of reliable statistical study.
I can tell you that my midwife is approaching 900 births through her career, and has sadly lost one baby and no moms, and that is sad to think of but that number is many times better than my nearby hospital. She also has a c-section rate around 3%. Again, she could be a statistical anomaly, but if I chose to analyze the data the way AGOG has, I could say "homebirth is 30x safer than going to my local hospital!" or whatever.
Anyway I hope that all helps somewhat. When people tell me "you're brave!" I say, "you're brave for going to the hospital!".