"I don't know in which human society you grew up, but my parents taught me that there is a duty to help others."
Don't get me started on cultural relativism. I really agree with you here. People ought to help each other, absolutely. But in that necessary since, they don't have to.
"I think you underestimate the number of people in human society."
This was just one of many examples of the same phenomenon. It is caused by the idea of diluted responsibility. Although, it is also influenced by the culture, the anonymity of the participants, and all sorts of other factors.
I should point out that you can't leave your wallet on the street in NYC and expect your money not to be stolen, either. My point with that story was that human society does not do the right things. You can't use human society as a measure of what is good. That should be pretty obvious. Just look around.
"True, assuming that you alone have the right and privilege to define who owns what. The entire definition of "property" is something society came up with. It doesn't exist in nature as a "right", only as something that can be forced on others as a rule.
And yes, you are at fault if you refuse to cure someone even though it is in your power.
But why don't you try it out? Wait until you are in a situation where somebody could die unless you helped and then tell that someone's mother than you didn't help because you had no duty to help and we'll see whether her instinct is to agree with you or to agree with me."
The first part is more or less saying, "Give to Ceaser what is Ceaser's." I agree.
You are not at fault. Certainly, though, someone might be upset by their son's death and looking for someone to blame. Why not a doctor? Why not the government? I would save the person to begin with, even though I don't have to. (I like to think I am a good person.) But if I didn't, sure, I would definitely lie about being able to have done it. People would not understand that it was the disease that caused death, not the unpaid doctor who stood by and watched. That does not change the fact that it really was not his fault.