It is easily possible for tetras to eat other tetras. Many kinds of tetras are fish-eaters...in fact, some of them specialize in it. Consider that piranhas, African Tiger Fish (Hydrocynus), the Wolf Fish (Hoplias), the so-called Fresh-water Barracuda (Acestrorhynchus), and the scale-eating Exodon are all relatives of the tetras.
That having been said, I don't recall ever seeing the Black Tetra (Gymnocorymbus ternetzi) being accused of being much of a problem in the community aquarium. Most references consider them to be peaceful and ideal community tank members. Then again...they ARE living animals and don't always behave as we expect them to.