What would be different about the family room on the next level down? Presumably that one would be intended for family of patients on the next level down...
Was that literally what they told you? "Administrators" and "you need to leave"?
Because often times in hospitals, the family areas double as a sort of consultant area for patient's family to speak with doctors and occasionally lawyers if matters of a will need to be addressed. Particularly outside of ICUs where the family cant meet with the doctor in the room.
There is not even a 0% probability that US hospital administration decided to save money by inconveniencing themselves in anyway.
Literally not even 0%. Not anywhere in the vast and deeply corrupt US medical system is a single hospital administrator, anywhere, that would make that decision.