Does it also apply to non-telephone conversation?
In Florida, the law makes no distinction between protected oral and electronic communication:
Florida Statutes 934.03-934.09: "It is unlawful under for a person to record a wire,
oral, or electronic communication unless all of the parties to the communication have given prior consent to such interception."
I expect it is the same in the other 12 "two-party" states.
In any case, it is the person seeking to record who creates suspicion, not the doctor refusing. Recordings can be tampered with. I am sure all of us have experienced rare patients changing prescriptions, notes, lab slips, etc. to their advantage. Recorders are red flags, IMHO.