A very interesting concept and I wonder if it has been used as a defense. In reality, you would have to ensure that the aired song is the exact same recording as that downloaded, otherwise you are taking from one set of musicians, recording staff, etc., over another. It would truly have to be apples-to-apples.
At the same time, I pay monthly for dozens of music channels as part of my base "cable" package (DirecTV, actually) and therefore have the personal use rights to those songs, do I not? All it would take is the technology to capture them in a usable format (separated by song, an indexing system). The RIAA has its tax on us through the products we buy and while it might be pennies individually, I'm sure the aggregate amounts are significant.
We also know the recording industry has lost class action suits but in a reverse flow of the pennies analogy, pennies are all we got back while trial lawyers and professional plaintiffs reap the benefits. I hope the next class-action settlement has as a condition the unconditional clearing of all the music on the original WKRP episodes and we get to see them again!
The RIAA would still have a problem with that I bet. They like Microsoft have this idea that just because you bought it, doesn't give you the right to copy it, even for backup purposes.
Simple, get some cables from Radio shack.. (or Wally World)... RCA plugs will do... if your sound card on your computer has an input (most do nowdays)... Now most these inputs are single jack, so you will have to have a adaptor for the RCA cable to a STERIO input for your sound card... Radio Shack...
Then get a program like PolderbitS (http://www.polderbits.com) and record away... I used this method to record all my records and cassettes to mp3 format too. Lots of fun... be sure to record all your stuff to a DVD every so often so you don't lose it with a computer crash...