Car beds are really a last resort sort of thing.
If she uses the On Board and the baby is under 4 pounds, it's technically misuse. However, I'm more concerned about the harness being fitted correctly (straps not falling off the shoulders, straps at or under the shoulders, harness able to be tightened all the way down).
My main concern is that if she is that tiny and also has a weak heart, that she might desat really easily in an infant carrier. I am sure the hospital will do a car seat challenge before the baby is discharged.
If I were the parents, I would purchase either the Onboard35 Air Protect or the Chicco Keyfit, and be prepared that my baby might not pass the challenge in the nursery, at which point she'll have to rent, borrow or buy a car bed.
To put it bluntly, car beds are not ideal in terms of car seat safety. They don't offer anywhere near the protection of a rear facing infant seat or convertible. They should only be used if using a traditional seat is an actual danger to the baby's safety, and then only as long as absolutely necessary, minimizing car trips to ones that can't be avoided.
I believe only two car beds are currently being manufactured...the Cosco Dreamride and the Angel Guard car bed. I don't know that one is 'better' than another.
Merritt (the company that makes the huge special-needs forward facing seat Roosevelt) is releasing a new car bed designed to accommodate bigger babies to 35 pounds. It's something she might want to look into if the baby doesn't show signs of passing the car seat challenge within the first few weeks. It's insanely expensive (800+) and probably something she could get medical insurance to cover if her medical insurance covers durable medically necessary goods.