I think you are confused what skin in the game means. Pilotes and startup founders are among the professions with most skin in the game. If they crash their plane/company they die/go brankrupt (or at least lose time and money) with it. That pilotes die in case of a plane crash is probably the main reason why air travel is so safe.
On the other hand doctors have, compared to their patients, no skin in the game. If the patients health gets worse or the patient dies the doctor stays unharmed. This is partially the reason for overtreatment in medicine (the other one being the asymmetry between the rewards for positive/negative effects of treatment vs. no-treatment.)
On the other hand doctors have, compared to their patients, no skin in the game. If the patients health gets worse or the patient dies the doctor stays unharmed. This is partially the reason for overtreatment in medicine (the other one being the asymmetry between the rewards for positive/negative effects of treatment vs. no-treatment.)