Canon has not been selling refurb 5D MK III's. They usually let them pile up for a year or so. The Used cameras that B&H sells are not Canon refurbished. We may see Canon refurbished 5D MK III bodies at B&H, and Adorama before they appear on Canons site.
Exactly. The 70-300 L was released two years ago, yet it only showed up on Canon's refurbished site a few months ago. Some products, mysteriously, never show up on the refurbished site. For example, the 200 2.8 L prime (which is more than 16 years old) is never listed, even though there must be thousands of them out there that would be good candidates for refurbishing.
Although the 5DII was listed on the site for a couple of years, it has really only been consistently available within the last year.
Point being, there is no consistent or predictable pattern for what gets listed and when it gets listed.