One of the main goals in nursing is accident and death prevention. That's why we talk about using helmets and wearing your seatbelt. Honestly, some of us would like to see trampolines outlawed because they are responsible for so many childhood injuries.
We also don't like to see anything around a child's neck that would pose a risk for strangulation. Things like this would include wearing a sling at night. We generally don't recommend this for concern that the child may get caught up in it and get strangled to death.
I explained my concern to her that I thought they posed a significant strangulation hazard and whatever perceived benefit they had for teething pain would not outweigh this risk in my mind.