I think that is an excellent question and it is one that I wonder a lot too! OK now I lose from square one-I compliment you on the quality of the question then I conveniently add myself in as a co-recipient of the credit of the compliment. How convenient!
As best as I could guess thinking about it, I think apparently all acts of humans are inherently selfish-even donations. Robert Ringer's old 70's pop philosophy books, "Winning Through Intimidation" and "Looking out for Number One" would see them this way-and I mostly agree. It takes mind-bending, a hefty dose of detailed thinking and humility to go there.
I have considered that in a universe that appears to be absent absolutes, there seems to be an exception to every rule. In humans that might be forms of insanity-whereby people take crazy actions because their facilities which process self-interest may be malfunctioning. The old saying, "take my offer before I come to my senses and change my mind" could be sort of a way of thinking about this. I am sure if you looked at that particular example you could shoot holes in it but the idea is that it may be possible for people to be unselfish through mental illness. Consider also that people who smoke or do other poor habits usually make an irrational choice whereby they take an action they erroneously judge will be a source of pleasure to them them when it really is not.
I've considered that some people could be disgusted by human nature and even reality and want to rebel against it. The entrapping idea that one cannot forfeit selfishness, it seems to me, might tempt certain philosophers and priests to experiment with the possibility of breaking this barrier if they were in the proper frame of mind to. Especially when one consideres the finite nature of life (nothing to lose trying because we all die anyway). Again, superficial examples of this principle might be seen in such people as martyrs, hermits and monks. They seem to be attempting to do this but I am still not sure whether or not they harbor a perspective that somehow they will benefit.
Advancement of humanity through Darwinism comes through error (perhaps as mentioned above)-probably not willful error. I would also add that while people are concerned with their well being, it could be possible that humans who have achieved their well being sufficiently may stop seeking it though selfishness. It might be that we don't even have the intellectual abilities to understand a paradigm without selfishness even if we are partly participating in it without knowing it.