It also involves intent to cause harm. As the legal system has repeatedly shown, a person's death, however tragic, could be the cause of manslaughter, or a defensible accident. In this case, the "perpetrator" may only get probation or a small amount of jail time. Manslaughter charges demonstrate the willingness of the legal system, and therefore our society, to sometimes, and under certain circumstances, view a death as a mistake and with no malice. Under that light, a doctor is not choosing on his own to take the life of an innocent patient with the aim to cause harm, which would be required to make his actions murderous. He is, instead, innocently complying with a request from a terminally ill person to end his pain. And since murder requires such aim to cause harm, and the doctor is not aiming to do so, the doctor does not commit a murder when taking part in these requests. Additionally, the doctor's actions are morally defensible because it is not moral to let someone suffer knowingly. Therefore, physician-assisted suicides increase dignity in death, and can be legally consented to by both the ill and the ill's family members.
It has always been the altruistic behavior of god-fearing people to not knowingly let someone else suffer. If one realizes that there is a person in need of help and that your services will relieve that person of his or her pain, then it is expected or required that you help. In this specific circumstance, a person is inflicted with an illness that will surely end in a painful and therefore, undignified, death. If one possesses the ability to help (e.g. physician, nurse etc.) then it is that person's moral obligation to help. This physician is not murdering a patient; he is freeing a person from an extremely uncomfortable state. It may be helpful to think of the classic children's film, "Old Yeller". In this movie, the child decides that it would be far more humane to kill his beloved dog than to let him die a painful death.