Even then it's not true altruism because you're doing it because you know it to be right and you (selfishly?) want to be the kind of person who does the right thing.

I don't think it's possible for apes who evolved and outcompeted other apes in the endeavor to become the dominant species on a planet to be truly altruistic. At least not without a lot more cultural, social, and possibly biological evolution, if ever.

Doesn't matter though. What difference does it make how "true" one's altruism is?