I can't speak about B&H refurbs, but I did buy a couple of refurbs back when I got my 10D. They were factory refurbished from Canon and came with all the bells and whistles like new.
And three in a row were defective. One had a big cluster of dead pixels, the next could not focus properly, and the third had really wonky flash system - sometimes wildly over exposing and sometimes not going off at all.
I came to the conclusion that Canon must just be giving returns a quick once over and then repackaging them as refurbished. I gave up on buying refurbished after that.