So I was trying to find it again, and as it turns out, the authors of the song were known as Double Dee and Steinski, aka Doug DiFranco and Steve Stein, a couple of media biz 20/30 somethings in NY at the time. There's plenty of info about them, including interviews and a spot in the turntablism movie Scratch.
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Given the common broadcast origin of cut-ups and samples in songs, I find it remarkable that a Brooklyn DJ duo could put their ideas into a song that resonated so well for us for completely different reasons. Growing up in Dallas, we found it ominous and on some level subversive to hear a song that flagrantly spun a day of infamy into an arty rap song. Plus you could kind of spaz out to it.
You don't need pirate radio to get Steinski anymore, it's available at Amazon. Following decades of legal obstacles, it has recently been released for the first time.
Or hear it here.