This seems universal.

Most hospitals have VIP rooms designated, some even VIP wings and suites.

You really think Bill Clinton didn’t get special treatment for his heart surgery years ago? He didn’t even check himself in. His staff and the hospital would have coordinated all that, and taken steps to protect his privacy. I’m sure the staff who took care of him were all hand selected. Even down to whomever cleaned the room.

Your poor ass gets whatever is available. If available, you get whatever doctor is on duty.