True greatness doesn't need rings.
True but it's icing on the cake.
I don't know if you mean in the big picture or as far as being a great athlete is concerned, but I don't think there are too many truly great players in any team sport that didn't at the very least get a shot at a ring. For example, Barry Bonds is a first-ballot Hall of Famer for sure, but by reaching the World Series in 2002, he escaped the distinction that is currently hung around Cub legend Ernie Banks' neck: "Best Player Never To Reach the World Series."