I don't at all believe that. In fact, it's not that I just don't believe it. It's that I know for a fact there is such a thing as an absolutely selfless act. A well developed sense of empathy is, I believe, required in order for a person to be moved to do things for absolutely selfless reasons; and not everybody's sense of empathy is the same as everyone else's.
There is a part of the brain that's associated with a well developed sense of empathy, and it has been observed through brain scans. That part of the brain is more active in people with a highly developed sense of empathy.
Everything I ever did for my children involved expecting nothing back from them (other than respect, which I also showed them and believed they deserved as well). I just answered a similar question to this and elaborated more on how mothers do selfless things.
A far smaller and simpler example would be this:
If I go to the HP forums and see that someone needs help I'll try to be helpful to them. That's it. It's just a wish to help someone. A lot of people just live their lives naturally trying to help, or give, just because they see someone needs help; think how easy it is for them to help, and see no reason not to. What do I get in return? Nothing as far as earnings or traffic go. In fact, I risk being a fool because "half" of the stuff on the Internet is make-believe or sleazy. If I write a long answer in attempts to be helpful, I risk having someone think I'm a long-winded blow-hard who "wants attention". I'm a grown up, though, so I don't care. I do what I think is right, and I do what I'd hope someone would do if it were I, or someone I care about, asking for help or hoping to get grown-up thoughts on a serious matter. (By the way, I'm not the type to ask for serious opinions on things; so I'm not hoping someone will remember and reciprocate at a later time either.)
A lot of people do things for others because they think/know they can, and so often it's so easy or effortless for us to help. So, again, why not help? What else have we got to do in this life that's so important that we can't/won't help others when we can?