Yui created The Blue Thing.
When Kayaba locked her away, Yui found a way to help players indirectly. However because she was so isolated and because of her limited view on humans, The Blue Thing sometimes does more harm than good. Kayaba indirectly told the Moonlight Black Cats of Kirito's bug.
How else could they have known about said bug? Either Asuna or Klein told the Moonlight Black Cats of Kirito's bug.
Asuna would either want to try and help Kirito, to show he wasn't alone. Klein would go spreading the information around for the hell of it.