I can't say what the Buddha's perspective is, because I don't believe during the time of the Buddha they had such things. However, I'll give my perspective if you want, based on what I understand about the moment of death, and how important it is for Buddhists.
I am not an organ donor. Why am I not an organ donor? It's not so much that I'm not generous and don't want to help people, but the moment of death is my time. It's a very important time. I don't want anybody interfering with my body, because I still may be around. I don't want the possibility that there's extra stress at that time that may distract me, or pull me back, or whatever it is. So I'm having Compassion for myself by not allowing anyone to interfere with my body when I'm dying. They may say, "the brain is dead," so they may say, the body is basically dead. However if the body is not dead (i.e. the heart's still beating), then I am not dead, as far as I'm concerned. If they start cutting into it, I don't know what my reaction may be at that time, because I haven't experienced it yet, so I don't want to interfere with that process. I would like to die naturally.