My answer is that they are bound by law and their organization in which they work for (duty and ethics) to save a person's life, regards of the wishes of the person. For a medic arriving at the scene, they could be seeing an accident victim, a suicidal person, or just a victim of a violent crime, etc. So all the people who said that it's because they "have" to otherwise they'd face legal and civil consequences (including being sued by the victim's family, friend, or acquaintance, etc.), that is true too. If I recall, an old time member @TiredHorse used to be an EMT so he would probably say the same as well. He (when was an EMT) was required to render aid regardless of what he thought about it.