we tend to think that we're selfless beings

That's news to me.

the sole reason we act selfless at all is to make other people think we really are selfless

That doesn't describe me. I sometimes act in ways that are detrimental to me and beneficial to others, out of a broader conception of my own self-interest: I figure that those actions are beneficial to my own projects, properly conceived.

I most specifically don't want people to think I am exploitable (which is one interpretation of "selfless"). I do want people to think of me as someone with whom it is desirable to cooperate.