Everything everyone ever does can be viewed as self-interested in the appropriate lens, but it's for precisely the same reason that that lens doesn't give you more information on how to predict people's behaviour.
A father risks his life to save his daughter. Did he do it for his daughter? Or did he do it because it made him feel better? Or to avoid feeling terrible if he didn't act? Or because genetics compels him to take care of offspring sharing, on average, 50% of his genetic distinctiveness?
There may be a causal chain in these things, genetics -> love -> joy of helping, fear of loss from not helping -> acting on behalf of another.
But we lose much of our descriptive, analytic and predictive powers if we insist on only looking at what we think are the first movers in this chain. It's not productive to try and predict the weather on the basis of quantum theory; for practicality, we look at the system at higher levels of abstraction, with their own conceptual bundles, and yes, their own names.
So I can agree with you that, in the most facile and base senses, altruism is not a "proper virtue", and that humans are "intrinsically self-interested". But I can also say that some humans are more altruistic than others, and that some humans are less self-interested than others, because saying these things expresses more information than trying to describe how one human seems to have a causal chain whose self interest leads him to seem paradoxically less self-interested and more altruistic, etc. etc.
In other words, I'm talking about personality at the conceptual level of personality, using its generally accepted meanings of words, rather than pedantically hammering away at first principles of selfishness.