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A little filling-in - It's not immediately clear why this is so infamous; stopping a song and playing another, while a bit jarring and probably unprofessional, isn't usually the stuff of legend.

Elvis was specifically forbidden from playing Radio Radio because of its (in my opinion, fairly mildly) controversial lyrics - it dealt with EC's dissatisfaction and scorn for the record - and radio, duh - industry. I guess Lorne Michaels didn't want to ruffle anyone's feathers.

Elvis, being the iconoclast that he is, agreed not to play the song, but proceeded to deliver a big ol' "Fuck You, Buddy" to Michaels, in the process increasing his television fame and exposure.

This E2 UPDATE courtesy of wedgeantilles: Michaels's reasons for trying not to offend any radio owners was rather primary to his interests; SNL's owner at the time did in fact own several radio stations. Thus, the obvious bad publicity of basically insulting one's sponsors to their faces. Of course, Elvis was never one to shy away from bad publicity - remind me to tell you about how he got labeled a racist for a good 3 or 4 years, and all the publicity that came with that...
GilloD says On your Radio,Radio node: While I agree that there were definite political overtones to the whole affair, a recent special on SNL musical performances had Lorne Micheals saying that he had no problem w/ Costello playing "R,R" and that the entire thing was blown out of proportion. Shrug. Stick with the legend :)

In this humble noder's opinion, it is not at all difficult or uncommon for people such as Michaels to, 20 years after the fact, go ahead and claim that there was really no big deal and we're all just pals. Then again, it certainly is common that pop culture events get sensationalized and blown out of proportion. In the end, GilloD has the right idea: stick with the legend; and the world you live in might be a little bit more interesting.