Elderly three-toothed dog prefers to sit ON things. Especially square things. Much like cats all over the world who will sit in boxes or even in shapes constructed of tape on the floor (thank you, Internet, for the plethora or photographic evidence of such occurrences), if there is a dishtowel on the floor, or, perhaps, a computer bag, he will make himself comfortable there instead of on the tile.
He's an old dog. We let him sit wherever he likes.