I just got myself a refurbished 6D and I wanted to add a couple points here. First, it looked and felt 100% brand new. Not a scuff or scratch, and the image count started at 0 (although I haven't checked the shutter count with the fancy checking programs). The only thing that looked off was they used an odd-sized peel and stick film over the rear LCD. It has been so long since I bought new that I don't remember, but I presume they are generally sized to fit, and this one was a little wonky. But otherwise, it looked completely pristine.
Second, I bought my refurb from B&H, although the listing clearly specified that it was refurbished by the manufacturer. It came in the same kind of packaging that the Canon refurb store uses and included all the same 1-year warranty info. I presume that the 1-year warranty is not limited to purchases from Canon only. I haven't seen anybody discuss this specific point anywhere, but both B&H and Adorama sell Canon refurbs.