It is a well recognized phenomenon, but it still brings me up short when I see it. The issue is that when life support is removed or a patient dies for other reasons, family members often want to make sure that the attending physician does not feel too upset by the event. Perhaps this is some kind of transference reaction, but I think it is more a case of generosity of spirit emerging from the particularly close relationship that develops during these end-of-life cases.
I recently received a note from a colleague whose relative had died after a difficult hospital procedure. He wrote to tell me about the case and said about the physician: "He seemed very upset. He is a good and conscientious man. Please check in on him and make sure he is OK."