This analysis is not deep enough.
First, I don’t argue against the proper usage of the GR+. I already agreed that in some situations you are supposed to use your best judgment, and perform as you would like others perform if you were in a certain predicament.
In this scenario, you should consider the following possibilities. When someone is in dire need of help,
and is able to articulate her wishes, those wishes should be obeyed, if you are certain that she is in the full command of her faculties. If she wishes to be left alone to die, that is her prerogative.
If she cannot do so, then you do whatever is the best for her, according to your best judgment. If you are unqualified to render proper assistence, then the best line of reasoning leads to call someone who is qualified.
In you scenario, this is not the case. You were qualified. To say that you would not want to get help - which will cause temporary pain, but allow the proper treatment administered in a hospital is nonsense. If that were the actual case, you would deduce that she is not in the position to make a sound decision. Temporary pain or permanent disfigurement is an easy dilemma to solve.
Once again, I don’t argue with the “spirit” of either the GR+ or the GR-. GR+ is easier to pervert. You example of how to pervert GR- is insufficient.
Some questions cannot be answered with a sound-bite.
Yes, that would be the typical short-term reasoning. And I seriously doubt that you could get away from “just about any crime”, though criminals usually don’t believe that they will be caught. But, nevertheless, many people use “your” version of the Golden Rule. They run over anyone else, just to pursue their own goals. And they are not necessarily “injured”, they are simply arrogant and selfish. Why did God not instill his values in them? Where is the “natural law” in their “heart”?
I should have known better than to ask it, I guess.

Now, can you give me some
secular reasoning why you think that all possible intelligent races (no matter what genetic predisposition they might have) would arrive to the same set of desirable behavior? The Catholic answer is easy to guess. But I am interested in some secular reasoning, if there is any.
Absolutely! This is precisely my point. You and I and everyone else has been indoctrinated through our formative years. Our value system is “forced” upon us, by the surroundings we have been exposed to.
Going back to the medieval Japanese society, even those who were oppressed believed that the Emperor was of divine origin, he had the mandate of heaven, and could institute any kind of oppressive society. After all, you don’t question God, why would they? And their society was fundamentally different, it was based on the forceful rule of the strong ones, and meek acceptance by the oppressed ones.
I said that the GR- can be substantiated by mathematics, as an optimal strategy based upon game theory. To that you replied that game theory could be used to substantiate genocide. I seriously doubt that, and I am a mathematician, well versed in operations research, game theory, etc. If you are another mathematician, you already know that. If you are not, all you have to do is invest about 4-5 years in college education, and then you will see what I mean.