One thing to keep in mind about Kentucky fans...they care WAY more about Tennessee than we care about them. That's not to say that we don't care about Kentucky or consider them a rival, but we've always focused more on Alabama, Florida, Georgia, and even Vanderbilt. Growing up in the 80s, Auburn was my 2nd most hated. I like the Kentucky rivalry, but it's down the list.
Our historic rivalries are informed by football (as is the case with most schools in most states). So Kentucky's historic greatness in basketball carries less weight than a football power. Until my sister went to UK and married a UK alum, I had no idea the hatred was so strong. They HATE Tennessee. I was like, dude, chill. You're just Kentucky. I never spent much energy hating UK because they were a sad little football program that had to settle for being good in basketball. To my BIL's credit, he and his friends will admit it. They hate us because we've always dominated them in football and been able to beat them more regularly than anyone else in basketball over the years. Plus, they don't border another SEC state.
So yeah, they're going to obsess over Tennessee and when they win (and more when they lose). It's a huge deal. Then they'll go on Twitter and tell us "We're your Super Bowl!" without intending the irony of it.