The pair, who recently announced their departure from the band, allegedly claim that frontwoman Williams took control of the band they had formed and began meeting with record labels without them.
In a blog post, they supposedly wrote that Williams released a statement about the brothers quitting the band without their permission, adding: "Zac and I wanted to be the ones you heard it from. I want to be honest with you guys about how this band formulated from day one. I did not think Hayley’s version told the whole story."
The entry goes on to claim that Williams was signed as a solo artist to their label Atlantic, and her father, who was their tour manager, often threatened to "pull the plug" on the rest of the group if they complained about the way they were treated.
The entry also says that the brothers were uncomfortable with some of Williams's lyrics, which often conflicted with their religious beliefs.
They wrote: "Hayley presented lyrics to us that were really negative and we didn't agree with. For example, 'the truth never set me free', which contradicts what the Bible says in John 8:32, 'and you shall know the truth, and the truth shall set you free'."
A statement from Williams last week said: "For the last year it hasn't seemed as if they've wanted to be around anymore."
A spokesperson for Paramore has since claimed the post is a hoax and was not written by the Farro brothers.
However, in a video message posted on YouTube, Josh said: "Hey guys, Josh here. I just wanted to let you know that the blog that was posted was from me and Zac.
"I know there's a lot of rumours going around that it wasn't from us, but it is. I know that makes some of you happy and some of you unhappy, and there's not much I can do. Hope it finds you well, see you guys."