Maybe I’m getting old, but I think its naive to think that selflessness is anything other than a purposeful act of will on an exponentially diminishing cost-return curve. In other words, one can try, but true selflessness is probably impossible.
I think people want to be truly selfless and that probably matters more than if they really are.
I think this question is like chess: If you are thinking too many moves ahead, everything becomes a calculated strategy. So, if you are playing to win, there is no room for anything but. Yet, not everyone plays ONLY to win, I think.