True. My cat would like me to run up the backs of armchairs with him, and go out hunting lizards in company.
He goes to the edge of the woods and meows and looks back at me. So we go for walks. Then he darts up a tree and wants me to come up there with him.
I am not as domesticated as he thinks. In fact I am a bit feral still.
NiMH cat does that.
He also brings home live prey to teach us how to hunt.