I believe in my heart of hearts that the Lego Batman movie exists in DC and that it was created by the batfamily as a way to throw off the conspiracy theorists
Maybe the superhero forums were getting too close to realizing their identities again. maybe one of their injuries had accidentally gotten spotted by the paparazzi. maybe they were just running out of plausible alibis. maybe they just wanted to be funny.
Bruce gave the world the "do the butts match" meme. His children give the world a cinematic masterpiece.