I don’t know whether or not there was any issue with JP II and a feeding tube in his own care, but if he was offered the use of one and denied it, this is not, according to my understanding, euthanasia.
One of the points of the Natural Law is that we are but humans participating in God’s divine law, which is intrinsic to our nature, hence, it is the Natural Law. Through this understanding, if one is facing the end of his life, he can choose not to undergo treatments which may prolong that life. He can instead choose to suffer or to just accept God’s will and await his death by the course of nature.
Euthanasia would be the removal of something that is keeping someone alive or intentionally seeking death. It’s the principle of double effect: if the Cause that is sought is death, it is wrong. If the cause that is sought is relief of pain, and there brings with it a chance of death, then it is not in itself wrong.
Regarding feeding tubes, JP II wrote a document on the conditions of people in a permanent vegetative state and stated that the use of a feeding tube is not considered “extraordinary means.” Extraordinary means, as someone quoted earlier from the Catechism, can be refused or removed.
A feeding tube, as JP II stated, is not an extraordinary means because it is not a method, nor does it offer a cure. Rather, it is something that provides nutrition and helps someone uphold their human dignity. As such, it ought to be used in cases in which there is nobody to speak for a patient. So, to withhold a feeding tube from a patient in the emergency room who has no representative to make medical decisions would be intrinsically evil in the eyes of the Church.
The feeding tube issue seems to be one that, under certain conditions, Must be used (as in the case above), but can also be denied as a way to accept God’s will and to prepare for a natural death.