In the instance of a shoulder dystocia, we don't know how long babies have before they die. I mean, I've been at two shoulder dystocias - one was 7 minutes from head to birth and the other was 4 minutes. Both babies were fine. If you have a baby who is seriously depressed and oxygen deprived BEFORE the birth of the head, that could compound the chances of successful resus, but even then, you can typically resus a baby - there just might be some brain issues if the lack of O2 was severe and prolonged.
That statement is just total bunk.
I feel so good about waterbirth with big babies because moms can assume a variety of positions to help ease their baby out without being on their back or tailbone. The water helps with perineal tears, etc.
If a baby, big or small, born or still in utero, experiences serious lack of oxygen, it will attempt a breath. That is why meconium aspiration syndrome happens IN UTERO and not with the first breath, as thought. So, if the head is out, baby could attempt a breath if there is serious problems, but it would be very rare and not at all life threatening. Because the chest is still in the vaginal canal, the lungs cannot fully inflate. Chances are, it would just take some extra time or maybe some blow-by O2 or some puffs to get baby going.
I just had a sticky shoulder 11lb 9oz baby and she got on hands & knees in the tub with her butt out in the air and I worked baby free. No problems. In fact, as soon as the shoulders were free, the baby rotated right out into dad's hands.