Everything (quite a lot) I have purchased from Canon Refurb was essentially new. I think it is Canon's response to the grey market. I suspect if something is not selling well in some country around the world, Canon ships it to their refurb store and sells it without the box (which was labeled in the language of the originating country). That keeps stuff out of the grey market and also directly competes with any stuff that does get into the grey market. The warranty is essentially the same as a new purchase, so definitely the go-to store if they have what you want in stock.
I don't believe that is where the refurb stock comes from for a second. Don't forget the demo units and returns all have to go back to Canon, they also have all the cosmetic parts to make anything look 100% new again, and the ability to reset motherboard shutter counts and anything else they want to do.
I also don't think Canon care too much about the grey market, if they did they would do things to shut it down. Things like Nikon where they won't repair, even for money, cameras and lenses not originally imported by Nikon USA. Canon Japan owns Canon USA and as far as the world economics of the thing goes every sale is a sale to Canon Japan irrespective of the final destination of a specific body or lens.