LOL---That has always been my favorite part of a Ribeye.
Whenever we split a Ribeye I always give Mrs Bear part of the center eye, because "It's all nice red meat without fat".
And Me being the nice guy that I am gets stuck with that outer par that's a Tender, Juicy, and Fatty.
Bear
I think your wife, and mine, are kindred souls!
Mine likes the center lean part medium rare, so I get the "Scraps" off her steak, and even medium rare, they are better than the dry lean eye.