I understand CEV. What I don't understand is why the programmers would ask the AI for humanity's CEV, rather than just their own CEV.

The only (sane) reason is for signalling - it's hard to create FAI<self> without someone else stopping you. Given a choice, however, CEV<self> is strictly superior. If you actually do want to have FAI<humanity> then FAI<self> will be equivalent to it. But if you just think you want FAI<humanity> but it turns out that, for example, FAI<humanity> gets dominated by jerks in a way you didn't expect then FAI<self> will end up better than FAI<humanity>... even from a purely altruistic perspective.