Milk has casein which obviously is a protein. This falls into a protein fining agent which will fine bitterness or tannin. I believe casein finings will remove the most from a cider or wine in comparison to other protein finings. It is reserved for harshest bitter notes.
It makes sense that the book referenced apple champagne because a lot of bitterness or tannin at champagne carbonation(5-6 volumes) will be unpleasant to drink.
Hope that helps.
Garrett