I agree with you. LE and doctors are reluctant to give death information over the phone. LE wants to be able to gauge reactions in person and physicians for the reason you describe above.
We've gotten a phone call where we were only asked questions such as: This is Officer Joe Blow from ABC Sheriff Dept. do you know someone who drives a beige Honda year 19xx? Is the license plate XYZ 123? Can you describe the owner? Do you know where we can reach that person? When did you last see or speak with X? All the while I was asking what happened? Is my sister okay? Is she dead? Was there an accident? Is the in the hospital? Is she dead? HE WOULDN'T ANSWER ANY QUESTIONS. My Dad then got on the phone and all they would tell him was that her car was involved in an accident. We assumed she was driving of course. We were freaking out because he wouldn't tell us anything. 1980's didn't have cell phones. She finally called us freaking out herself because she had driven to a classmates house to carpool to another city for a class. Her car and several surrounding were hit by a hit and run driver, she came back from class to find totalled cars.
![Frown :( :(](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Until she called, we didn't know if she was hurt or dead, the exact location of her car, etc. If he had simply said that several PARKED cars were damaged by a hit and run driver, we would have had somewhere to start at least.
When my brother was hit while on his motorcycle, the doctor called from the hospital to tell us we needed to be there. He wouldn't say anything about his condition
other than we should get there as soon as possible. We were 15 miles away, but our Mom was several hundred and we worried about her driving.
So, fwiw, I believe it's possible that MS told TS' family as soon as he was notified. I could also believe the doctor friend would have told MS that he found TS passed away, but maybe no details in that first conversation, maybe not even that she was murdered, I don't know.
I'm looking forward to being able to hear the interview so I can know what was said and how it was said.
People's emotions can color recollections.