The Reshetikhin-Turaev construction take as input a Modular Tensor Category (MTC) and spits out a 3D TQFT. I've been told that the other main construction of 3D TQFTs, the Turaev-Viro State sum construction, factors through the RT construction in the sense that for each such TQFT Z there exists a MTC M such that the RT construction of applied to M reproduces Z. Is this true for all known 3D TQFTs? Does anyone know any counter examples?