“They probably could have won the case against Fox, since it clearly falls under the “fair use” exception to copyright law.”
Unless Jason Aldean is giving away his music and performing the song for free, then the fair use doctrine does not apply.
Again, as I said to the other poster who already tried to claim that, it’s a common misconception but it isn’t actually true. There are plenty of cases where fair use applies to for profit work as well.