The "controversy" comes from one-eyed desperation of fans who can't accept it when things go against them. Wouldn't Albion/Wolves have more/similar claim to being the oldest rivalry?
No. Albion never gave Wolves a second thought until about 1990.
Actually in terms of "local" proximity the Hawthorns is a lot closer to Villa Park than to Molineux as well, so more of a local rivalry should exist.