The main asteroid belt, which inhabits a relatively narrow annulus approximately 2.1-3.3 au from the Sun, contains a surprising diversity of objects ranging from primitive ice-rock mixtures to igneous rocks. The standard model used to explain this assumes that most asteroids formed in situ from a primordial disk that experienced radical chemical changes within this zone. Here we show that the violent dynamical evolution of the giant-planet orbits required by the so-called Nice model leads to the insertion of primitive trans-Neptunian objects into the outer belt. This result implies that the observed diversity of the asteroid belt is not a direct reflection of the intrinsic compositional variation of the proto-planetary disk. The dark captured bodies, composed of organic-rich materials, would have been more susceptible to collisional evolution than typical main-belt asteroids. Their weak nature makes them a prodigious source of micrometeorites-sufficient to explain why most are primitive in composition and are isotopically different from most macroscopic meteorites.