The twins, 17, were banned by producers from taking part in Saturday night's first live show after Josh was accused of attacking and sending threatening messages to an ex-girlfriend.
He was previously accused of striking her but denied that in a statement, saying: "A fight broke out between me and another male at a party. Amelia, along with others, tried to break it up. She was accidentally knocked in the process. It was never my intention to hurt her or put her in danger - and this situation is way out of my character."
Now, the twins have issued their first statement since the live shows, telling fans: "Today, we have had a tough day with a false allegation. Don't believe everything you read, both Amelia and Josh will be stating the truth.
"The truth always wins."
It's unclear whether Josh and twin brother Kyle will be suspended further from the show or return for next week's second live show, which has a Motown theme.
A rep for X Factor said on Saturday night: "As was said at the top of the show due to circumstances that have arisen Brooks Way didn't perform last night. This relates to information which has been given to the show regarding one of the group.
"Until we are in a position to do so we won't be commenting further."
The twins were removed from the X Factor mansion and placed at a nearby hotel while producers investigated the allegations. They were pictured leaving Fountain Studios in London on Sunday after alleged "crisis" talks with bosses about their future.
Brooks Way are mentored by Louis Walsh in the show, who also looks after groups 5 After Midnight and Bratavio. He's made no comment on their situation.
If Brooks Way are permanently axed, it means Louis only has one group left on the show as Bratavio were booted off by viewers and the judges during Sunday night's live results show.
X Factor continues Saturday and Sunday on ITV.