It took a bit of reading, but I think I see the source of our misunderstandings.
The article says, "Electrons in an ss orbital have a greater shielding power than electrons in a pp or dd orbital of that same shell … For example, consider an atom of carbon whose electron configuration is 1s^2 2s^2 2p^21s22s22p2. The two electrons in the 1s1s orbital of C will do a better job of shielding the two electrons in the 2p2porbitals than they will of shielding the two electrons in the 2s2s orbital."
The article is really saying, "Electrons in an ss orbital have a greater shielding power than electrons in a pp or dd orbital of that same shell for electrons in the next higher shell".
It isn't saying that a 2s2s electron is more effective at shielding another 2p2p electron than a 2s2s electron.
It is saying that a 1s1s electron is more effective at shielding a 2p2p than a 2s2s electron.
This explains the dip in ionization energy on going from Be to B. When you go from a 2s2s orbital in Be to a 2p2p orbital in B, the 1s1s electrons are more effective at shielding the 2p2p electron of B.