The recommendations are not all that new- the blanket one has been around for more than a decade for sure. The no bumper rule is a new one- I think the stores will stop selling those adorable crib sets- but when my oldest was a newborn, I already knew that is was risky and bought breathable mesh-like bumpers instead of the padded kind.
I believe it does have to do with smothering- a baby can end up with his face pushed into a padded bumper or pillow or stuffed animal and not be able to realize he cannot breathe and extricate himself.
Correct me if I am wrong, but I think that SIDS would be when a baby stops breathing for some unknown reason. Having a blanket obstruct his breathing Chas v’shalom is a known reason. Being overheated is a risk factor for SIDS though, so maybe that was the connection between blanket and SIDS.
So save the tallis for wrapping up the kids at his upsherin.