Let's take JHJ in his own words to find inconsistencies and maybe get a hint at an answer. Skip the opinions if you want, I tend to speculate.
Dispatch
On May 2, Aran underwent a surgery. On that day, Employee “B” sent a message to Jeon Hong Joon.
B: CEO, they said Aran’s surgery will go well and she will be moved to a hospital room to recover. The surgery is currently going well, but I will continue to monitor as they said we have to watch her condition.
B: I’m going to give the other members a break while Aran recovers, is that okay? May 10 to May 28. The other members would need to return to the dorms by May 28.
Initially, Jeon Hong Joon countered by only giving them a week off, and employee “B” responded.
Jeon Hong Joon: That’s too long. What will you do if there’s an accident? Give them a week off and then have them come back to the dorms. I’m concerned about an accident regarding their safety. Give them a week. After they go back to the dorms, give them more personal improvement time.
B: Ok. I was worried about the same thing, but there were requests from both the members and their parents. Also, Aran needs to rest for at least two weeks but she complained to Ahn Sung Il that she would only get one week of rest, out of worry.
In the end, Jeon Hong Joon told employee “B” to have them rest until May 25, giving them just over two weeks instead of one week.
Opinion: At this point in time, the girls likely haven't sent JHJ proof of contents citing their complaints about financial transparency & health concerns, etc. Note that after this point JHJ will be more mindful to appear concerned about their health, which he's clearly not if he only grudgingly gave Aran the two weeks after major surgery.
On June 9, Ahn Sung Il and Jeon Hong Joon had a conversation regarding FIFTY FIFTY’s involvement with the Barbie movie.
Ahn Sung Il: It will definitely be good to do the Barbie movie. I’ll meet with them first to try to persuade them and I will communicate with Aran.
Jeon Hong Joon: It’s good for you, the group, and the company, but since it’s also a matter of dealing with a health issue, communicate well with both the parents and the members so that there are no misunderstandings~!!
Jeon Hong Joon: With such a good showing its frustrating that they cannot do anything these days~!
Ahn Sung Il: Ok. Aran listens well to my opinions anyway so I’ll check her condition first.
Ahn Sung Il: I’ll go to personally see her mother.'
Opinion: Note the concern for health expressed as he's becoming more careful about digital footprint, which actually helps him in this case. But clearly he's excited to proceed with Barbie and the two men are in agreement.
"Barbie" OST music video filming was canceled
"...ahead of the filming [for Barbie MV], the members of Fifty Fifty sent Attrakt a proof of contents regarding the termination of the exclusive contract. In response, Attrakt CEO Jeon Hong-Joon suggested that they postpone the schedule by saying that we should shoot the music video after the problems between the members and the company were sorted out. Then, according to Attrakt, CEO Ahn Sung-il said that if he couldn't proceed with filming the music video, he would quit the Fifty Fifty job."
Opinion: In his own words, JHJ was responsible for cancelling Fifty Fifty's activities as the team was ready to go at this point. CBX stayed active after filing their lawsuit and even during their CEO's "external forces" mediaplay. JHJ made the drastic move to stop all activities. Why? It must have become clearer at this point the girls might actually file (they did on 6/19) and he needed to prevent the lawsuit from happening above all else including inflicting irrevocable harm to his own group and ultimately his own interests as well. And it was only after the lawsuit was filed did the girls finally get access to financial records. What is in, or not in, those records that he's so afraid of that a lawsuit might be able to reveal?
Fifty Fifty’s company gives response to ‘Barbie’ MV being cancelled
“It’s true that at present, we have been unable to film a music video for the ‘Barbie’ OST. Member Aran was sick and had to undergo surgery, and she needed about two months to recover, so we were unable to schedule a shoot for the music video. But then the current situation happened, so it became difficult [for us to film a music video].”
Opinion: It's clear he's blatantly lying now. Aran was ready to go and the current situation including SIAHN's departure didn't "happen" to JHJ. JHJ was the immediate cause. But this portrayal paints the picture of JHJ as the helpless victim. Barbie MV and all subsequent activities had no chance of ever happening. But I'd bet financial loss or even the loss of the group are the least of JHJ's worries.