No, patients do not have a "right" to refuse a room change no matter how much as they think they do. When I worked in the hospital, we once had to have security and the Nursing Supervisor come to the floor because a patient's family attempted to refuse a room change. It was our room which doubled as our comfort care room... a dying patient was being admitted and needed that room. The patient being moved out of it just didn't want to move into a double room. There's not a hospitalized American patient out there who doesn't have a list of 17,000 reasons why they are entitled to a private room over anyone else. (I say American because I noticed when I worked in the hospital that patients from other countries- mainly underdeveloped ones- didn't mind nearly as much. I recall having to put an admission in with a patient in the middle of the night, the family was from India. The charge nurse apologized to the father for interrupting their sleep and giving them a roommate so late and his response was "This is a hospital, we expect to have a roommate.") My favorite excuse for people trying to refuse double rooms when I worked in the hospital was "but she just had brrrrrrraaaaaaaiiiiiiiiiiiinnnnnnnnn surgery." Well, guess what? This is the Neurosurgery floor, so did everyone else here.
I've never known a Charge Nurse to decide on room changes just for the heck of it... if rooms are being changed it's for a reason. Say you have 2 double rooms... they're both filled with female patients. One patient from each room is discharged and now you have 2 open beds which are your only 2 open beds on the entire floor. Then 2 males need to be admitted to the floor... what do you do? Your only option is to move one of the female patients into the room with the other so they are now roommates and then put both admissions in the same room. You have one negative pressure room on the floor and have to admit a patient with suspected measles. The patient who is currently in that room does not require a private room- no choice, they have to move.