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