That's how it works in the best case. Unfortunately, medical research is not a perfect science. Realistically, with many medical treatments, you can't have a double-blinded study. With chemotherapy, the side effects will often quickly tell you what treatment you're receiving, and a treatment like for example extracorporeal photopheresis can't ethically be placebo-controlled or double-blinded at all. What are you going to do, hook half your patients up to a machine that will do nothing but run their blood around a bunch of tubes for hours for no reason?
And you can't get a "large sample size" of patients with rare cancers or diseases by definition. Sometimes, the best you can do is a case study of ten patients who agreed to try your treatment because the other option was death. Quite a few medical advances have been made that way, actually.
This is not a question of being "rational", and there's no right or wrong answer. People make trade-offs between quality and quantity of life every day. Do I want to quit smoking, drinking, drugs, and take up sports, etc for a chance at a longer, healthier life? Or do I grab all the fun I can, and if it costs me ten years, oh well? The right decision will look different for every person - and it's not black or white, but a continuum.
The choice of how much pain is worth it for how much of a chance at a longer life is going to look different depending on your religion, your responsibilities, your age, your experiences with pain, your family, your culture, etc. And yes, of course the cost of treatment will factor into that decision for both the doctors and the patient.
Medical research benefits hugely from terminally ill patients who are willing to try anything for even two more months of painful life. There are a lot of of experimental, highly dangerous cancer treatments that could never be justified if not for the fact that even without them, the patient would have about two months to live.
That said, there will always be enough patients who want to fight for their life no matter the cost (see other comments on this page for evidence) that if you'd prefer to die in peace, you certainly shouldn't feel obliged to play the guinea pig for science.
To everyone considering a "NO CODE" tattoo after reading this story: Don't. If you're really that serious about not wanting to be resuscitated under any circumstances, wear some kind of bracelet or necklace with those words on it, and, just as importantly, a recent date, and contact info for a person who knows your exact wishes. Make sure to update the date regularly.
Medicine changes, and so do your life circumstances. If you're presenting an EMT with a ten-year-old, faded tattoo, you're placing them in an awkward position due to the lack of context. Is this a decision you made ten years ago and got stuck with, or are these your current wishes? They might end up disregarding your wishes just to be safe. A bracelet with a recent date will be much less ambiguous.
And remember, with all medical decisions, you want the ability to change your mind when medical advances are made or your circumstances change. Tattoo removal sucks.
And you can't get a "large sample size" of patients with rare cancers or diseases by definition. Sometimes, the best you can do is a case study of ten patients who agreed to try your treatment because the other option was death. Quite a few medical advances have been made that way, actually.