I always thought that SIDS stands for "parents likely accidentally killed their child through negligence or error, and a prison sentence seems too harsh". So we make it a medical condition instead of a crime.
Some infants respond to a drop in oxygen by stopping breathing all together, instead of breathing faster or trying to get more oxygen. It is thought this is leftover from time in the womb: https://www.frontiersin.org/articles/10.3389/fneur.2015.0022...
Anything that reduces how much oxygen the infant gets can potentially trigger this. So while it might be "there was a pillow the baby managed to roll into", it could also be a mild allergic reaction, acid reflux, a respiratory virus or insufficient air circulation. None of those things would be enough to be a "cause of death", because they were just the trigger for the infant's brain deciding to stop breathing.
And why would that be incorrect?