Spin connection in Chern-Simons theory

While I was reading Witten's paper on Chern-Simons theory and the Jones polynomial, I tried to understand the underlying geometrical considerations in more detail.

I understand the need for a counter term to regularize the action functional. I also understand conceptually why a gravitational Chern-Simons term would make sense. However, two points remain unclear to me:

• Why choose a spin connection/connection on the spin bundle? Could one not, e.g., choose the ordinary Levi-Civita connection on the 3-manifold?
• (Presumably related) Why does one actually need a framing/global trivialization? The gauge-Chern Simons action is also well-defined without trivialization (cf. Global Chern-Simons forms and topological gauge theories). The only reason I can see why this could matter, is because it could influence the "canonical" choice of spin connection, but then we get back to the first point.