In the olden days I could get a refund of a non-refundable ticket for a medical reason with a doctor’s note. Is that still the case?

In the olden days, when non-refundable also meant non-changeable, that was indeed true. However, that practice was virtually eliminated when airlines began allowing the value of non-refundable tickets to be retained for future use, minus a change fee. Some airlines may reduce or waive the change fee with appropriate documentation. Acceptable documentation varies by airline, but typically includes emergency room or hospital documents rather than just a doctor’s note.