IIRC death by suffocation is not confirmable. That is why there is suffocation-avoiding sleep advice, such as avoiding fluffy blankets and pillows, mixed in with general SIDS prevention advice like keeping the temperature of the room low and placing babies on their backs to sleep.
It's possible that the tragic death of the little girl has been attributed to the headband because of the placement of it at the time of death whereas it could have been an ordinary cot death.
That said, heavy fabric over the mouth and nose could easily obstruct breathing and perhaps it wouldn't take very long for a baby to reach distress.
Either way what an awful thing to happen :(