There's absolutely no reason that LLM providers can't provide equivalent guarantees. Distrusting Sam while trusting the existing providers makes little sense.
BTW, putting mental health aside, many doctors today are using LLM tools to record the whole conversation with the patient and provide good summaries, etc. My doctor loves it - before he was required to listen to me and take notes at the same time. Now he feels he can focus on listening to me. He said the LLM does screw up, but he exists to fix those mistakes (and can always listen to the audio to be sure).
I don't know which company is providing the LLM in the backend - likely a common cloud provider (Azure, Google, etc). But again - they are fully HIPPA certified. It's been in the medical space for well over a year.