I agree. I tend to think the doctor's office may have been given some additional details by the person who inquired and were told why they were were inquiring and why they were worried.
What I'd like to know is who made the inquiry to the doctor's office and was it a phone call or was it made in person? Was NUA aware of the extent of the marital problems? In an interview, she indicated how shocked she was when CW told her about a separation when she called him.
Whoever contacted the doctor's office by-passed CW completely. I believe NUA arrived at SW's house at noon or shortly after, and it appears she already knew the doctor's appointment was missed. She didn't call CW until 1:00 or after to ask him if he knew where SW and the girls were.
I think that whoever contacted the doctor's office knew about the extent and severity of the marital problems and may have already had some big concerns about CW as he was by-passed entirely on this, and he was the husband (and father) and in normal situations, I think the husband and father would be called before the doctor's office was contacted to find out how the appointment went, and to see if he knew where his wife and daughters were.
What happened is as far from normal as it could possibly be.