Satan was right when he said: And everything a man has, he will give it to save his own skin. It's not a bad thing necessarily, it's merely an animal thing - survival is your prime instinct. If you attempt to commit suicide by hanging and you don't break your neck or restrain yourself, you will unconsciously attempt to save yourself, same goes for drowning and is also the reason baby's can swim.
Put yourself in the situation - you or your kid has to undergo an operation and there are 2 choices, certain death imposed by people that can't even explain their doctrines themselves or a chance of survival based on sound, proven science. Blood transfusion is not always the answer but these days (DISCLAIMER: I work in the medical research field but I am not a licensed medical professional) most doctor's will try to exhaust any viable other option especially if their client asks for it however doctor's do not want you to die nor are they agents/worshippers of Satan so if they say it's your last option, you should believe them and make a choice accordingly.