In our research, we haven't found any reputable medical or scientific study to support claims that glycerin interacts negatively with the n-Ha.
Glycerin is used widely in all sorts of toothpaste as a humectant. It prevents toothpaste from drying out in the tube and becoming unusable.
The important note is that glycerin is water-soluble and dissolves easily. It is removed by saliva if left on the teeth, and the act of brushing removes any remaining glycerin from the surface of the teeth.