I've always heard the same thing. Used to be big in the field trials myself. I may have heard of your dad or known him.My dad was a fox hunter when I was small and he was alive. He won a couple of big field trials with his dogs. And he told me that a grey fox was a member of the cat family hence the tree climbing. And a red was a member of the dog family. I have no idea if that's true now, but I believed him then.