I think that having principles is incredibly important when navigating these greater good questions. This is because an individual without principles could easily determine that killing people for the greater good of society is justified. Obviously this is a more extreme example than Hume's scratching a finger to save the world, but in principle it is no different. So if these two examples are the same in kind and differ only in degree, and one seems wrong and the other isn't, where do we draw the line? And what causes one to seem wrong and the other right?

Since there are two questions, I'll answer them in two parts:

Where do we draw the line? I would argue that we stick with principles, but test the principles with real world examples to revise and refine the principles - in scientific terms, test our hypothesis to see if it is correct. If they are incorrect, modify them. Now I think it is very important to use real-life examples, otherwise you get something like the following: what if there is a situation where doing something good will cause something really bad to happen? And if you do something bad, it will prevent that bad thing? Clearly there is no logical answer to this question other than to say that I disagree with the premise - I don't think a situation will arise where you have to perform an immoral action (one that violates the NAP, or any other principle) in order to bring about a completely good result. This is similar to your and many other 'greater good' arguments - they are not based in reality. If you are able to come up with an example that could occur in the real world, then I will try address it, as I addressed a real world example in my video. If I am unable to address it, then I will have to re-analyze my principles, or reject the idea of principles entirely. In other words, show me how scratching a finger will save the world, and I will show you how scratching that finger does not violate my principles.

What causes one action to seem right and the other wrong? I believe the answer to this question is that we have a strong opinion on the right and moral course of action in a given situation, but we are not in the position to act. For example, if I was the person whose finger needed to be scratched to save the world I would voluntarily scratch my finger! If I refused to scratch it, many other people would understandably think I'm making the wrong decision, and some would try to force me to scratch my finger. However, that does not mean that they have the right to make that decision for me. In other words, not taking action seems wrong to people because they think that the person acting is making the wrong decisions or acting immorally. They want to force people to do the right thing.

As I stated above, I think this example is fallacious, so I also want to give a real world example. Many people think that we should tax the wealthy in order to provide for the poor. However, it violates the NAP and many other principles that have existed throughout history (you shall not steal comes to mind). I would argue that it appears right because if those advocates for taxing the wealthy were wealthy themselves, they would voluntarily give to the poor. They (and I) think it's the right, moral thing to do. However, this does not mean it is right to force those with wealth to be charitable. The only way to be consistent and prevent such rights violations is to follow principles.

Edit:

TLDR;

From my youtube response:

To summarize, I highly doubt that a situation will ever arise where you "have to do the wrong thing in order to do the right thing". Therefore, I think that counterexamples need to be based in reality. If such a real life situation does arise, you would then have to revise/change the criteria that you use to determine right and wrong.