AZ,
Do you have a link to the article? I used to live in Arizona and while they've had some good games recently I'd have to say UA-ASU isn't anywhere near Duke-UNC or the other rivalries you mentioned.
As far as UK being a rival to any program, it hasn't been recently, and it remains to be seen whether Calipari's one and done and reload recruiting strategy will work at UK. He did it on a smaller scale at Memphis but from this class at UK it appears he is willing to recruit multiple one and dones in each class. There is something to be said for continuity and team building, which will be lacking at UK for at least two years.