I see no problem with people moving to the village at a later date and becoming one of the Ordonians. Link's house was on the outskirts of the village, so perhaps his parents or otherwise ancestor that moved there was someone who emigrated there from Hyrule. And since those communities are fairly close knit and weary of outsiders, their house had to be outside the proper village at the time. Even though Link was accepted as a member of the village there would be no need to build another house closer to the village as it was good enough, and the home of his family. There would be no need to change.
Generally Link is the outsider that enters Hyrule in all the games that give him some kind of origin. He always comes from very humble beginnings, but that is a traditional standard in a fantasy story. In ALTTP he lived very far away from Kakariko, OoT he lived in the Kokiri Forest, Outset Island in WW, with his uncle away from the village in MC. The developers seem to like having Link discover the wide world of Hyrule at the same time as the player. When you are completely new the the area and have never seen it before, it makes for a much greater level of exploration in the game.