modular tensor categories - Do all 3D TQFTs come from Reshetikhin-Turaev?

If you have a 3d TQFT, with no anomaly, and which goes down to points, and where things are sufficiently finite and semisimple, then I think you can show that it comes from a Turaev-Viro type construction on the 2-category Z(pt).

If you have a 3d TQFT, possibly with anomaly, which goes down to circles, and where things are sufficiently finite and semisimple, then I agree with Noah: Z(S^1) is a MTC and the RT construction on the MTC reproduces the TQFT.

Relating these two statements, TV(C) = RT(double(C)), where C is a 2-cat, double(C) is the Drinfeld double (or maybe center), TV is the Turaev-Viro construction, and RT is the Reshetikhin-Turaev construction.