Our great UK basketball historian, Jon Scott did research on this topic.
Following is an excerpt and a link:
Below is an excerpt from the second of a four-part interview with Paul Bryant in the August 22, 1966 edition of Sports Illustrated. This passage discusses his leaving Kentucky and the reasons he gave for it.
Well, we won at Kentucky, and I don't think I'd have ever left if I hadn't gotten pigheaded. It was probably the most stupid thing I ever did. I could have had just about anything I wanted, and Mary Harmon loved it. We had a social position coaches seldom have - good friends with Governor Wetherby and all - and we lived right there near the Idle Hour Country Club. Mr. Guy Huguelet got us an honorary membership, and that's a club that some people wait years to get into.
We had built a new house, and I was on the verge of making some real money. I had turned down half a dozen good jobs. A member of the board at LSU said to me,
"Dammit, everybody has a price, Bear. What's yours?" And I put it up there pretty good for those days - something like $25,000, a home, a TV program and everything-and he said,
"It's a deal." No school could do that, but he said he'd give me a contract through his company. Then I backed out. Alabama people came to see me and I wouldn't even talk to them, and Texas A&M and a couple others also approached me.
http://www.bigbluehistory.net/bb/bearbryant.html
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I went off and left Kentucky with the second best squad I ever had. Blanton Collier came in there the next year and had a winner. We had the new home and all those goodies, and it broke Mary Harmon's heart. Worse than that, when she got off the plane at College Station, Texas she turned white.
Texas A&M is a great educational institution with rich traditions, but at that time it was the toughest place in the world to bring players to because nobody wanted to go there. Don Meredith told me before he went to SMU,
"Coach, I'd love to play for you if you were only someplace else."