You can know why the analogy holds without having enough detail to compute with it. Likewise you could have a picture that is truly part of you, but where not all of it is, so that you only get halfway there.
It is pretty easy to understand why the Doppler effect happens (at least, if you happen to be exactly my past self). You can easily have the ability to independently come up with the explanation without being able to derive the formula.
The way I think about it is it’s based on what I care about. I am in fact unwilling to do certain things to save the life of someone who is threatening suicide and blaming me, because I care more about myself, and I am fundamentally okay with caring about myself in that way. If, say, my best friend made some stupid mistake that put her at risk of great harm, I would be doing the heroic responsibility thing because I care a lot about the outcome.
It’s fine to care about yourself! The principle of “I am obligated not to harm you, but not obligated to help you” is a fine one. The point of heroic responsibility is to see what I could do in cases where I do want to go all out to achieve some outcome.