Are more dangerous than home birth. That claim is what NG wanted evidence for. I don't think it is a red herring to expect you to support that claim.
You pointed specifically to the first result of the search and even after I pointed out it did not support your claim you doubled down claiming that it did.
As for low risk pregnancies and home birth it appears to not be a higher risk to the child and a number of studies support that. I have read some that criticize the methodological approach of these correlational studies but I am not sure I agree with them. I have no problem with this portion of your post