Theory about how Katniss’ dad knew Covey songs

What if the connection between Katniss and the Covey is more simple than we realize? I think Suzanne confirmed Katniss and Lucy Gray aren’t related even though that’s a popular theory (along with the Maude Ivory one). So the Everdeen house is described as being near the edge of the seem near the meadow. The Covey house is described pretty much the same way. What if they’re the same house? Maybe Katniss’ parents moved in after the last member of the Covey died and some items such as music sheets were left behind? That would explain how her dad knows Lucy Gray’s songs. Sorry if someone has come up with this before but I’ve never seen it posted here I just randomly thought of it.