Suffocation. Soft bedding can definitely increase babies risk for accidental suffocation. This could be wrongly classified as SIDS. A firm crib matress with a standard sheet is low risk. Those cribs you see at pottery barn with all the really soft fluffy items, including expensive plush crib bumpers are dangerous. A thin bumper is ok, a plush one is not!
One theory. One theory has been offered that flame retardants in the mattress is a cause. This is obviated by placing the infant in the supine position and this position has now been accepted as a major preventive, (not necessarily related to a mattress effect).