If you read into their "proof" for the belief its a lot of stuff that is "its implied" from the text. Even the Ezra one, which is the only real direct one, they say that the way he says it means its obviously been in practice for far longer before it was written.

So it sounds like some oral tradition they had that they added to their religion and then they went back to pull a bunch of proof out of places it wasn't.

Like all things, its very Jewy and nonsensical. I'd say its their religion to do what they want with, but they don't follow it in any form that makes sense either.