"There's definitely more to the story. They don't arrest for an obvious accidental smothering, do they"
Yes they do.
As said, if an unexpected death happens and those present refuse questioning, then they are arrested.
If your baby died and you had another one of the same age, would you be thinking straight enough to want to leave your remaining child, or dead baby, to go to a Police station?
We had a situation in my family (I have written about this before), were it took months for the Mum to be cleared, her picture had been in a local paper. The baby died from a rare form of Broncolitus (SP).
There is another story about a baby killed by the Step Father, although the mother wasn't present at the time if death, she had been arrested and her subsequent baby, that she was pregnant with removed until the child was over a year old.
I wish that it was common knowledge that the arrest of Parents/Carers can be routine.