How can you be sure that emotions are really involved? Being instantaneous, I believe there is something else there, like how you stop before going down the cliff towards an almost certain death. Might it not be intelligence, saying that(not really having this monologue but xd) 'someone is in danger of getting hurt or even killed, saving her would spare her that'.
Isn't there the possibility of intelligence acting upon it and not emotion? That way there would be no 'me FEELING the need to save her'. I do not believe intelligence to be selfish, because
Sure, there has to be a challenge, a happening, for a reaction to be seen, but I do believe there are cases, if going by the impulses you mention in your fourth paragraph were, instead of accusing the car, seeing how it might not be intentional(maybe there was an animal being avoided resulting in this poor woman's situation) and not viewing it as 'at fault' at all, it all being unfortunate(figuratively speaking).
In the case you mention about accusing the car and there being emotions involved, yes that is selfish, but is all emotion selfish? Are all emotion concentrically spinning around the 'me'?
I'd say emotions is mostly conditioned to the challenge proposed, relative to the past experience and memory about similar events or preconceptions of such events. Thus remains the question whether these pure emotions you speak about are possible or not. I say, don't control your feelings, and controlling reflexes seems almost impossible, but in the case of controlling as a means to an end, I think it only imposes dullness and hinders intelligence, as control implies friction between you and the thing being controlled. Waste of energy more or less, in many cases. In all, does control not create more selfishness? More of 'me'?