I never thought about this, but looking at them I can obviously see the possibility of them being brothers.
This story really started to go around recently when Howie Mandel invited both Billy and Bill on his podcast at the same time to talk about it, unbeknownst to Bill Burr at the time, who was not very happy about the situation. It all ends well though, as you can see in this NSFW clip from the podcast where Billy explains the story, and it all makes sense now.
According to BIlly, and Bill, they each had a father who was mostly absent in their lives, and at one point Billy’s mom told him that Bill might be his half brother from his father, who had multiple families.
And in this clip they each share stories about their dad, seeing if they’re related or not.