It sounds like you primary concerns relate to infection control - whether your father or your family have any risk from being in the room with the other patient.
My suggestion is that you speak with the hospital's administration about what you heard the doctor say to the other patient and the related concerns. Double rooms sometimes create "incidental" disclosures that while they may not violate HIPAA can create other issues. See what the hospital folks say.
This response is intended to provide general information, but not legal advice. The response may be different if there are other or different facts than those included in the original question. See MKnutsonLaw.com for more information on why this communication is not privileged or create an attorney-client relationship.
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