The rule:
- “Who” refers to people
- “That” doesn’t.
Here’s a good illustration of why this matters:
Is he referring to the ex-wife or to the phone message? Ambiguity is bad except in poetry and lies.
A writing tip: pronouns are supposed to refer to the closest possible antecedent. That’s why I avoid pronouns. Too easy to lose track of the antecedent.
These are possible alternative sentences:
- …message from an anonymous ex-wife who told me…
- An anonymous ex-wife sent me a message that told me…
- An anonymous ex-wife told me…
I suppose I could add that the doctor appears to be violating patient confidentiality.