When I was a little kid, sometimes little boys would record songs off the radio. And we'd all yell "busted!" and laugh. Because it was technically illegal, though no one ever got in trouble. Or so we thought. Someone eventually did. But in Sony Corporation of America, et al. v. Universal City Studios, Inc., et al. (1984) the SCOTUS ruled it was still "fair use". Also when I was a kid, a teacher once told us not to sing "Happy Birthday" at your parties, because that was also technically illegal. And again we thought it was funny. It really wasn't again. Because someone did eventually get sued for it. Yeah, Warner Chappell Music had previously claimed copyright on the song in the US. But in 2015, the copyright claim was declared invalid in September 2015 by a federal judge. Because it was all so ridiculous, he basically said.
The fair use clause is what enables us to post up copyrighted material here without consequence. So long as it is used for educational, critical or satirical purposes it is legal. That's the law. And making a copy for yourself of a broadcast is also legal. In fact, if you don't copy something to make money from it, it's doubtful you will ever have to pay for it, unless it deprives the creator of their due profit.