Yeah, but it's weird for another reason as well. See, Fan Club was meant to reference Japanese Pop Singers, and the most popular examples of these are cute young women or female teenagers that wear "cute" outfits and sing songs that are, for the most part, simple and have incredibly wide appeal because of this, be it with guys, girls, kids, teens, or adults. It's basically the pop stereotype, even though many (and probably most) Japanese pop singers aren't like this.
The song itself, from the little Japanese that I know, is actually pretty faithful to the original, it's just how this really translates on a phonetic level that really makes it sound silly in English (well, that and the singer). In Japanese, it may sound similar and the message may be the same, even with some of the words and sentences translating perfectly, but they don't sound as silly because their Japanese equivalents don't sound that way in Japanese...if you follow me.
Oh, and I checked it out. The singer on TV and on stage are doing the same pose, but I can see where it looks like one is doing a peace sign while the other only has one finger up. What's really happening is that the singer is pointing her index finger and thumb, rather than her index finger and her middle finger. It does kind of look like a peace sign, but its clearer what she's actually doing on the TV.