What is the theory behind this? Does it keep the airway open, possibly linking SIDS to some underdeveloped neuromuscular issues?
There isn't much theory behind this statistical, case-control study. It's just a recognition of previously known risk factors that increase or decrease the likelihood of SIDS. From the Introduction:
"The reduction in the incidence of sudden infant death syndrome (SIDS) after the Back to Sleep campaign in the United States and other countries showed that sleep environment strongly influences the risk of SIDS,1 2 although the underlying mechanisms remain poorly understood. Despite the considerable reduction in the incidence of SIDS after this public health intervention, it remains one of the leading causes of infant mortality. Identification of new preventative measures to further reduce the incidence continues to be a priority. Some studies have reported that use of a dummy (pacifier) is associated with a reduced risk of SIDS, though few have examined the association in detail and in the context of other risk factors.37
"Dummies usually have a bulky external handle, which could alter the infants sleep environment by changing the configuration of the airway passage surrounding the nose and mouth. For example, pacifiers may prevent accidental hypoxia as a result of the face being buried into soft bedding or overlaying by objects (such as blankets, cosleepers, etc) by providing an air passage created by the bulky handle. Sucking on a dummy may enhance the development of neural pathways that control the potency of the upper airway.8 9"
Here's their take-home 'power points'.
What is already known on this topic
Sleep environment has consistently been reported as influencing the risk of sudden infant death syndrome (SIDS)
Use of a dummy during sleep has been reported as reducing the risk of SIDS
What this study adds
Use of a dummy during sleep was associated with a reduced risk of SIDS consistently across a wide range of socioeconomic characteristics and risk factor profiles
Use also reduced the adverse effects of a prone sleep position, sleeping with a mother who smoked, and soft bedding