You are thinking logically here. Always a bad idea when speculating about TSA rules. As with many TSA rules, prohibitions against sharp-pointy things are there to make people feel safe, rather than to actually prevent a tragedy. Did anyone really think terrorists were going to bring down a plane with knitting needles or nail files? As long as people can carry on a piece of glass (which breaks into very sharp objects) the rules don't actually prevent people from getting sharp objects on planes (and if you prevented glass, there are endless other things that can become a sharp weapon easily).
If I had to guess (and maybe I'm guilty of trying to be logical here) a vegetable peeler falls into the same category of knitting needles, nail files, dull scissors and other "acceptable" sharp-pointy things. They'll probably go through, but you always run the risk of a TSA agent who decides on the spot it's dangerous and makes you throw it out.