Canon have a number of EOS 5D MkIII refurbished bodies in their online store. My guess is that they don’t have many. In the past popular refurbished bodies have sold out quickly. Refurbished directly from Canon is usually like new. I’ve bough refurbished items from them in the past and they’ve been perfect. Their price is $2397.33. A new EOS 5D MkIII from B&H is $3149 and a new EOS 5D MkIII from Adorama is $3299, so buying a refurb directly from Canon will save you at least $750.
EOS 5D Mark III Body Refurbished from the Canon online store – $2397.33