In MOSFETs why is the gate-body inversion layer voltage able to create a conducting channel, yet the same source-drain voltage not?
why is it that the required gate-body voltage to create this inversion layer is so much lower than the voltage required to overcome the reverse bias?
  
  Or is it the proximity of the gate (and thus its field) to the area on the semiconductor it is trying to invert?


That's it. The gate is separated by mere 10's of nanometers from the channel by the gate oxide, whereas the channel length might be separated by µm's or more (depending on VDSmax), so the electric field from the gate is hundreds of times stronger.