Why? Because it makes no mention of it? Where in the name of God would there even be a place to mention it in all of Richardson's dialouge; just because we didn't find a holotape map of evry Enclave location or a total census of the entire population doesn't invalidate his existance, you know what didn't exist in Fallout, the Vault Experiments, yet they retconned them in. There were no physical people there so there was no need to mention it when he was talking about the vaccination; it makes perfect sense, satilite communications have clearly survived (F3) therefore I see no reason why they couldn't communicate. Eden could have in contact with the ENCALVE well before Richardson, they could have used his knowledge and machine-like infalibility to write a series of water-tight Ammendments to the US Constitution, they could have used him as a general data cruncher. Tell me why it goes against canon; in fact it fixes it, having Eden become President through legitimate channels such as the Succession make more damn sense than a military officer just saying, "Okay your smart, would you like to be the President?"
EDIT: The Shi aren't a proper government, the President of the United States cannot be so simply chosen; him being a ZAX has nothing to do with it, that's the point.