Why was there so much confusion when Mr. and Mrs. Eberhardt to get to the hospital?

The confusion is found in the fact that Roy wasn't actually the patient in the emergency room. Beatrice and Roy had taken Mullet Fingers to the hospital, but Mullet didn't want to give them his name because he was afraid they'd call his mother. Thus, Roy gave his own, and it was Roy's parents who got the news their son was sick.