It lies but not completely. He is not global like he says he is. The medkit has to be near him. I tested it last game, save scummed until medkit shows up near the doctor. I did have 1hp, though. Also, that didn't save the run.
currently its only doing it if medkit is adjacent which is wrong. The update this week will fix this! I couldn't say anything before because of doctor-medkit confidentiality.