Electron distribution in a C-S bond
I think your lecturer would have been more correct had he said that the carbon-sulfur bond reacts as if the sulfur is slightly $\delta^{-}$ and the carbon slightly $\delta^{+}$.  

Sulphur is a larger atom so it has more, loosely held electrons than carbon.  This means that a sulfur atom is more polarizable than a carbon atom.  Although carbon and sulfur have similar electronegativities, the effect of this increased polarizability for sulfur is that sulfur behaves or reacts as if the bond were polar.  Take the case of nucleophilic attack on a $\ce{C-S}$ bond.  As the nucleophile approaches, the $\ce{C-S}$ bond will tend to polarize because of sulfur's polarizability.  And in which direction will the bond polarize?  Electron density will prefer to shift such that it resides on the larger atom (charge to size effect), sulfur.

This is the same argument used in the case of a carbon-iodine bond.  Again the two atoms have similar electronegativities (carbon = 2.55, iodine = 2.66), so although the bond is not polar based on electronegativity considerations, the polarizability of the iodine allows the bond to react as if it were polar when a nucleophile approaches.