Ages ago, I worked in an OB/GYN office in the U.S. and one of the things I had to do was call patients to remind them of appointments. I was told, when leaving messages on answering machines or with people other than the patient, I wasn't to give out anything that might suggest the nature of the appointment, just saying that I was confirming the patient's appointment with Doctor X.
In your scenario, the nurse could give a message like that, saying, 'This is a nurse at Dr. X's office just calling with some test results. Please have Sue call us back.' The resourceful husband could always look up the doctor's name in the phone book and see that she/he is an OB.