I don't share any cancer specialists with my family but I was in that situation with another specialist years ago. I was seeing him for 2 years and then my Mum made an appointment to see him without telling me, he actually stopped treatment with me (and her) because it put him in an awkward position.
Some people just don't understand boundaries. Though I would guess that surgeons would see so many people that it may not even occur to them that you are related, unless one of you mentions it.