Final answer:
Dame Cicely Saunders was invited to Yale School of Medicine for being the leading authority on the hospice movement, revolutionizing care for the terminally ill.
Step-by-step explanation:
Dame Cicely Saunders was invited to become a visiting professor at the Yale School of Medicine because she was the leading authority on the hospice movement. Her work revolutionized the care for the terminally ill by introducing hospice care which aimed to provide death with dignity and effective pain management in a comfortable setting. This was a significant shift from hospitals being the primary end-of-life care locations and reflected a more humane approach to dealing with terminal illness, aligning with cultural shifts in the perception and management of death.