Willie's autobiography, Willie's Game, has quite a bit about his interactions with Fats. What you say above was certainly true for many years. But one of the last things Willie says about Fats is: "...to my surprise, I found myself growing fond of Fats. How could I not like him? Every time he opened his mouth I made money, and his mouth was always open."
I read that as well and saw it as a backhanded slap and also a perfectly reasonable thing to say. It's one of the things I have said to those who troll me here, the more you troll me the more I get to advertise and make money. And it's true.