Facility charges for holding a room while a resident is hospitalized and then returned to the same facility for therapy on Medicare?

My mother is 85 and suffers from Alzheimer's. She is has a private pay room in a skilled care facility. Recently she was hospitalized and had surgery after she fell and broke her hip. She returned to the facility after a week in the hospital and was moved to a "medicare room" in the same area of the facility. She has received therapy for six weeks. This was the 4th room change in a 6 month time frame. The additional 20% of her care is covered by additional insurance. I was told that I only needed to move what she needed to the "medicare room" and she would be moved back to her private pay room after she completed her therapy.
I have received a bill from the facility for the full private pay rate for the room they were holding for my mother to return to after her medicare stay was exhausted. My question is this. Is it appropriate and common place for a facility to charge the full private pay rate to hold a room for a resident that is required to move to a medicare room for the care and therapy she has been ordered, even though there is no care provided for that room, no meals associated with that room and no cleaning or maintenance of that room. The facility is full and I was told that if we did not paid the full rate for her private pay room while she was absent from it there was no guarantee that there would be a private pay room for her after her stay in her medicare room was exhausted.