33girl makes a very valid point. Most, if not all, of the AEPhi's from the chapter that was closed would have graduated by the time SAEPi was founded.
That said, it's still more than likely that this show will reflect negatively on AEPhi in particular, in addition to the greek system as a whole. People will remember that AEPhi used to have a chapter there, and will link SAEPi to AEPhi in their minds. SAEPi's website explicitly mentions the closing of the AEPhi chapter as part of its history. There is also the similarity in names, and SAEPi's link to AEPi, which a lot of people assume (wrongly) is a brother fraternity to AEPhi.
I haven't seen the ad... but why am I so not shocked that MTV is portraying sorority women as a bunch of party animals?? Whatever boosts their ratings, I guess.