Partially correct. Quite true that UK has to play in Freedom Hall.
UofL is a tenant in the Yum! Center as opposed to the owner. They have a lease in effect until 2044. The issue is that U of L negotiated such an incredible deal with the Yum! Center, that it stipulates that they have exclusive use of that building the day before, the day of, and the day after a game. You do the math, but that leaves very little time for outside events such as concerts, other sporting events, or shows.
Recently articles came out that say that the Yum! Center is in serious financial trouble, which may lead to local bonding issues. U of L's contract is so binding, and they get such a big cut of the revenue (Including 88% of luxury suite income, including NON-UNIVERSITY events), that the Yum! Center isn't making enough money to keep the lights on. I predict that in short order there will be a new lease contract negotiated if the Cawdinals want to be able to play in there with lights and heat.
The arena was built with the hope to attract an NBA team to Louisville, but UL's AD is a very shrewd guy, and got a hell of a contract with the Yum Center...so much so that it's causing the new arena to go belly up, potentially at the cost of taxpayers.