Milk contains nutrients such as protein, lactose and fat. Lactose belongs to carbohydrate and substance, and it will give priority to supplying a part of energy to the human body to save protein. The so-called "drinking milk on an empty stomach can't fully absorb nutrition" probably refers to the loss of protein, but it won't actually cause this situation.
However, some people with gastrointestinal function or congenital lactose intolerance should not drink milk on an empty stomach, especially not drink a lot of milk on an empty stomach. For example, some people will have abdominal distension and diarrhea after drinking milk on an empty stomach, and such people are not suitable for drinking milk on an empty stomach.