Lol, I just found the funniest piece of information while checking something regarding the KotR because I need to work on Mordred's reactions to people:

[quote]
Shards of the table can be used as catalysts for summoning Servants, summoning one among eleven of the knights based on compatibility with the Master. While it is believed all thirteen can be summoned, Arthur and Galahad are excluded. They are especially prized as catalysts during the Subcategory Holy Grail Wars of the Fate/Apocrypha world due to providing a high-quality Servant no matter who is summoned. Each shard is a holy relic, unique items that are likely never to appear again if destroyed. One such shard possessed by Kairi Sisigou is destroyed by Mordred, who has a certain disgust for the Round Table. [color=ed1c24][b]Though they look like regular pieces of worked wood, "heat" can be felt emitting from them upon touch.[/b][/color] As of the time of the Great Holy Grail War, the shards sell for very high prices on the market, but there are also many fakes sold as well.
[/quote]

Thus, we can conclude that Apocrypha confirms that the Round Table was a kotatsu. I can bet that Merlin is behind this, somehow.