You are right that SIDS is not the same as suffocation, but for this particular situation, the doctor was thinking of suffocation when he asked her to not have fluffy things on the bed. Heres some stuff from
Dr. Sears website that might put this in perspective.
HOW BACKSLEEPING HELPS
Why back-sleeping lowers the risk of SIDS is not completely known, yet here are some possibilities.
1. Back-sleeping babies awaken easier. Arousability from sleep in response to a life-threatening event is a healthy, protective mechanism and one that is thought to be diminished in infants at risk of SIDS. Back-sleepers arouse from sleep more easily and sleep less deeply than tummy-sleepers. Mothers have observed, and research has confirmed, that infants sleep more deeply on their tummies. Yet, sleeping more deeply does not mean sleeping more safely.
2. Back-sleeping babies have a lower chance of getting overheated. Overheating, possibly by interfering with the central nervous system control of breathing, is another risk factor for SIDS. Lying on your back leaves your face and internal organs exposed so that they can radiate heat more readily than when sleeping on your tummy. (That's why when your cold, you probably curl up on your front or side to conserve heat.) Also, front- sleeping babies are more likely to slip down under the covers than those sleeping on their backs, another factor that may contribute to overheating, since a baby's prime avenue for heat loss is through their head and face. In the back position, even the baby who slips down underneath the covers would be more likely to throw them off. The contact of a cover with the face is more likely to be noticed and protested by a back-sleeping baby than the contact of the cover with the back of the head would be in a front-sleeping baby.
3. Back-sleeping babies breathe more oxygen. When sleeping face down, a baby may press her head into the mattress or wiggle her face against a soft object. This can form a pocket of air around her face, leaving her to rebreathe her own exhaled air, which has diminished oxygen.
4. Back-sleeping babies are less likely to suffocate. Conventional wisdom has always taught that suffocation is a rare cause of SIDS. Yes, babies are sturdy little persons who, even as newborns, are able to lift their heads and keep their noses clear to breath. The often quoted "study" that even tiny infants have the ability to lift their heads and wiggle their noses clear of obstruction was not really a scientific study; it was more of an observation. Yet, new insights cast doubt on the rareness of suffocation. A growing belief among SIDS researchers is that many babies presumably diagnosed as SIDS may have in reality died from suffocation on soft surfaces
While no one knows exactly why the front-sleeping position is linked to SIDS, the overwhelming number of studies that all come to the same conclusion - back sleeping decreases the risk of SIDS - make it clear that for healthy infants, back-sleeping is safer. Parents should note that there are some medical conditions, such as gastroesophageal reflux or structural abnormalities of the jawbones and airway, in which it is safer for babies to sleep on their tummies rather than on their backs. Be sure to check with your doctor to see whether or not your baby has a medical reason to sleep on his tummy rather than his back.
BABIES WHO SHOULD SLEEP TUMMY DOWN
Be sure to check with your doctor to see if your baby has any medical conditions that necessitate front sleeping. Babies who should sleep prone are the following: • Premature babies with respiratory problems still in the hospital; sleeping on the tummy increases breathing efficiency in prematures with compromised breathing, but not necessarily when their lungs are normal• Babies with small jawbones or other structural abnormalities that may compromise the airway when sleeping on their fronts• Babies who have mucous-producing respiratory infections or profuse drooling associated with teething - if so advised by your doctor• Babies who are extremely restless and settle poorly unless sleeping prone• Babies who suffer from gastroesophageal reflux (GER).
Hope this helps. For me the decision was made for me. My Ds would not sleep if he was on his back unless I was with him. So for naps...on his tummy he went. But like I said earlier, at night, he slept on his side or on my chest. There is more about SIDS on Dr. Sears website if your interested.